Four lesser options, one major one.
Fast-forward the split party part. Don't dwell on stuff as much as you otherwise would.
Snack and bathroom break time. Shoo the other players off. This will serve as a cue to the sneakers that they should include everyone eventually.
Metagame, encourage the group to find ways to include people even when it's suboptimal.
Spring stuff on the other party to keep them occupied. Sure, if they just get a lead, they can wait to follow up, so make the action come to the PCs - someone kicks down the door or otherwise looks to interact with them NOW.
Give them all equal spotlight time. 5 minutes dealing with sneakers or interrogators, 5 with the others. They'll either start going to do stuff of their own accord, or they will, heaven forfend, roleplay with each other.
Number 5 is really my favorite. We've had plenty of great moments while half the party is doing something "important" and the other half goes to a bar and gets in trouble. All you have to do is give them the spotlight time, PCs are notoriously twitchy and impatient and will find ways to entertain themselves, "on task" or not.
My added thoughts based on your question edit.
You don't need to balance "in game" time. If one group went and did something for six hours, but real time that took five minutes, then you just need five minutes of spotlight time for the other group, even if that's five minutes of rousting a hobo and then 5:55 of "we go somewhere and hang out."
If they need ideas for what to do or you want to spring things on them - that's why God created random encounters, right? Either they self-motivate some mission oriented stuff, which you come up with, or they mess around in a tavern or go shopping, which you come up with, or they sit around looking glum till a land shark attacks them, which you come up with. You do anything you'd normally do to the full party, but ideally with slightly less kill. (Or not, if you want to dissuade them from splitting in the future.)
If they are content to wait in the bar, let them wait in the bar. Have fun bar things happen. People hang out in bars in real life, it's fun. And sometimes good and/or bad things happen, hence the larger than usual incidence of hookups and cop interventions in bars. All you need is for them to all be having fun and getting roughly equal "spotlight time" (time they get to actually do something at the game table).
Not everything has to be mission related or be a "subplot." They can just find out interesting things about the world they're in. If every story everyone ever tells them is a "subplot," then you get into a bad rut where their expectation is that anything that happens in the game world is FRAUGHT WITH MEANING, and it can't just be some guy BSing about how he fought a troll armed with a spoon once.
In my campaign, I make sure there's a healthy amount of "the world doesn't revolve around the PCs" stuff going on. Not only does it make for a realistic feel, but then when someone wants something to do, they have the expectation that "Hey, I can just go out there and go shopping, or find a bar, or find something to do - I don't have to be 'working through a plot element'" every damn minute of every damn day.
In my Pathfinder campaign recently, the party split. One half was going to do something on task and important. I don't even remember what it was and they probably don't either. The plan was to meet up at a known bar later that day. The other half of the party decided "we'll just go wait at the bar now." I roll a random encounter - giant cockroaches. They get to the bar, and the owner, "Ball-less Bill," an old ex-pirate with one leg, one hand, one eye, and apparently less then one thing down below, was standing outside the bar holding the door shut. "What's the problem?" "My basement flooded and there's these big ol' cockroaches running around in there! They're as big as dogs!" "We can take care of this! Stand aside, Bill!" The two PCs bust in and the cleric casts Call Lightning. The cockroaches are like CR 1/4, so they run all around and out into the street as the cleric blasts lightning holes in everything in sight. The fear of God is put into the local yokels, and the cleric gets an Infamy Point (the equivalent of a Hero Point in my pirate-oriented campaign). They yell "Wooo!" and go in and drink for free.
The other half of the party... They did something on mission. Got some information or something. Who cares. No one remembers that, but they remember the Great Roach Holocaust.
If you have proactive players, this shouldn't be a problem. If you have reactive players, then don't treat them like proactive players and give them 'things to follow up on.' Have the world turn, and its events happen around or to the players. If they decide to just go find another bar rather than chase out the giant cockroaches, fine, then make them choose whether they're drinking "bloodwine or dwarven grog" and go back to team A. Seems to me like you're overthinking this by requiring all events to be part of some big Mythic Plotweb.
Best Answer
In particular for your first bullet
This was originally the last section of my answer. I actually like it more than everything else I've suggested so now it's the first thing.
This is sometimes a hard solution for 3.5e, but honestly not as hard as it is for 4e for what I'm aware, so... You mention
This one has a way easier solution than changing your players mindset and designing complex encounters.
Challenge them in other ways than combat. I'm assuming your powergamer is optimized for combat, otherwise... Challenge them in other ways than the one the powergamer is making easy.
There are numerous other ways of challenging the players other than combat. Social interactions are an obvious one - make "encounters" that are unwinnable if they choose to strike instead of talk. Puzzles with complex traps are another - we have a puzzle tag. You can either challenge the players with puzzles or the characters, your choice. If you decide to challenge the players, you won't ever have a problem with powergaming that aspect of the play.
This also means you won't run out of content so easily. Essentially, make a different kind of content, one that doesn't get drained easily by optimized characters. If that is not your style, keep reading.
I will revive my experience from 3.5e for that question, adding some insight from 5e (because that's what I have been playing for the last ~4 years).
First things first:
Your players seem to want to play different games
While one player wants to powergame and optimize his character, the others want to... I don't know because you didn't specify, but it seems they either don't want to optimize or don't know how to.
Being the DM for two different groups that want to play two different styles of game is usually hard and, as the link suggests, not usually recommended. It is not impossible though. But yeah, for 3.5e (and I assume PF) it is harder than usual, since there is a lot of unbalancing there. If you are willing enough to a point of changing the system, 5e suffers considerably less than 3.5e and PF from this problem - and I would recommend the linked answer even if you don't plan into changing the system.
In particular, if your other players simply don't know how to optimize, the powergamer can help them with that. Then you can proceed to make encounters that are challenging for everyone because now everyone has an almost broken character.
If they don't want to, that's a bigger problem. Here are some things that you can ask the player to do and do yourself. The first two are for changing the characters he plays, which might not help you.
Ask him to play Enabler/Control characters rather than huge DPS
Treantmonk's guide to God Wizard explains the concept better than I can think. I've linked the 5e guide, but the important thing there is the introduction, where he states his reasons for creating his 3.5e guide. The TL;DR of the guide is: He was asked to play a optimized character, but the other PCs weren't optimized. After trying out a character that overshadowed their party, he decided to make a God Wizard.
This means he won't be able to solo encounters on his own. Everyone in the party will still feel useful, your encounters can be "normal" and he will be challenged by having to support his teammates that aren't optimized. As someone who mainly played Wizard in 3.5e and 5e, this guide (and the whole mindset) is awesome for playing an optimized character while making everyone else - especially new players - feel useful by themselves.
Handicap him
This answer for another thread frames it too well. Instead of optimizing the most and being the most ahead, he can instead optimize from a lower starting point - playing either underpowered classes or starting with lower stats or any other kind of handicap you want to give him. He will then have to optimize a handicaped character to get to "as good as" the other characters. There are ways to impose these handicaps on him yourself, like giving him less magic items (which 3.5e depends heavily mainly for martial fighters from what I remember) and other things. Make sure he agrees with that, though. Punishing players for whatever reason is at least a reason to discuss it, as can be seen here and here.
Different fights
This one may seem awkward, but it has worked for me. It won't work for every encounter, but for some of them, instead of putting the party against 4 Goblins, you can put them against 1 Goblin Leader and 3 Goblins. Then, since you are the DM, you can proceed to split the party and make the optimized character focus their time and effort in the goblin leader while the others are focused in the 3 usual goblins.
Essentially, rather than having one ancient dragon or 10 goblins fight the party, try to diversify the enemies in a way that the optimized character gets a larger share of the CR for him. Obviously this needs a) the optimized character being able to "solo" fights b) the other party members being able to handle their mini-fight on their own as well.
The split can be done either forcefully by you - traps, walls and whatever else you can think - or as a "suggested tactics" for the party.
This can also be done in a less impactful manner by making the guy with huge attack focus only on him, while the other creatures/NPCs/enemies focus the others. Yeah, you'll have to find some excuse for the optimized character being targeted by the more powerful attacks, and that will depend on the characters, their backgrounds and their way of behaviour, which are informations we don't have. But it is certainly possible to do while making it immersive.
As I said, I've done it before, but I don't recommend it unless everyone can agree to it. It leads to the game being way less cooperative than most are used to.