I hope they pass, and try to plot for them passing but I feel like I need a swoop-and-save always in the wings.
Ah, here we clearly have part of the problem. They're in a situation where they would fail most of the time if you weren't engineering things for them to succeed, so they should fail some or most of the time. If you feel bad for railroading them or for removing the challenge from the game by ensuring that they don't fail, stop doing that.
PCs don't need to succeed all the time, especially when the danger isn't lethal. Failure can be instructive and even fun! (Even, dare I say it, . . . "character building"?) Honor is so important in that setting that a moment of lost honor, a recognition that they aren't perfect in all things, can do wonders in terms of future character motivation. Plan for the characters to fail.
That is not to say that they should never succeed or not learn anything, though, but there are ways of doing that without having direct social-roll confrontations or even after failing at all direct confrontations.
First, don't worry about giving them a loyal subordinate with the social skills to take on the courtiers some of the time, and don't worry about fudging the rolls for him up or down if you have to . . . maybe he's talented but new and prone to rookie mistakes or getting rather old and not as fast or perceptive as he used to be. Also, don't worry about having him advise the PCs. However, his advice shouldn't just be "do this"; have him offer multiple options with pros and cons and let things play out from there. Heck, let him be wrong sometimes just so the PCs don't rely on him too heavily. (A sufficiently deep intrigue will have elements he couldn't expect, or that were expecting him. . . .)
Second, give them plots where their bumbling or social weaknesses are strengths. Have enemies overestimate them and plan for the wrong reaction from the PCs, have their bumbling somehow convince everyone that they know more than they do (spooking the enemy into making mistakes), have them accidentally round up all the right people for all the wrong reasons and someone confesses to the plot and then asks how they knew, or just plain have things come to a point where the villains are expecting some nuanced social reaction they can parry and the heroes decide to just charge in and take care of things the old-fashioned way.
There's one more option: The overestimated idiot at the center of a backstabbing circle. In social politics, this is where everyone tries to curry favor with the lord by telling on everyone else. As a result, the lord is spectacularly well-informed about everyone else's secrets and develops a reputation for being an omnicient badass when all they had to do was sit there and look stern and knowing. If your players can handle that kind of information effectively, they'll find ways of taking care of business without ever having to make a social roll they don't like.
I think that neither yourself nor your players, are playing Numenera. Warning signs such as "dungeon-making skills" and characters able to use 5 level of effort (wow!) makes me think that you are trying to play D&D with a different world and system. This will not work, as you clearly found out. This is an paradigm problem.
In any case, the true path to Power in the Cypher system is, well, the cyphers.
The whole point of Numenera is to use cyphers like they went out of fashion. After all, you gain many new ones all the time. Traditional hoarding will hold you back and make you less powerful. This needs to be clearly explained to the players: "Do not hoard, spend!"
So, do a silly one off encounter with different cyphers: each player plays their character but with a random set of cyphers. The aim is to defeat the obstacles in their path using those cyphers. The next iteration has new cyphers so forces the players to adapt. This should not take more than an hour per round. Do a few, and your players (and yourself) will get how it work. The aim here is not to defeat all the obstacles, it is to get used to spending cyphers. It should forces the players to think outside the box and come up with new and fun uses for their cyphers.
A good such encounter might be a physical fortress, a hostile guardian, some social interactions, and a combat against people using the same cyphers themselves in each iteration.
During game play, offer them many new and interesting cyphers. So, unless they use theirs, they cannot pick up the new ones. Sure, they can discard some to pick a new one but really, where is the fun in that? You are not playing a tactical board game (neither sarcasm nor insult implied) but a story game. Make sure you players know that their characters are not going to die because they spend that cypher last session.
If the players have a healing cypher (say it regenerates limbs), then clearly your next GM intervention cuts a character's hand. Said player can either take it, gleefully get a XP, and regrow a limb or be boring. Now, of course, another GM intervention that turn said arm into an obsidian black animated sculpture might work well -- think Hell Boy.
As a GM, you know what cyphers they have. Suggest to them to use them: "Alice, your character has a cypher that allows her to float. That might be a good way to get your bearings in this weird wood."
Finally, you need to talk to your players and convey the idea that they are responsible for building the world around them as much as yourself. Cyphers are one way to make it the commonly shared story more interesting.
Best Answer
Talk to your players
Just...step out of character for a moment and talk to them. There's no rule that says the DM can't help players remember the features their characters have. If you're more comfortable doing it outside of the game, then chat with them in private (in person, text, chat, whatever).
If you were trying to teach someone how to play checkers and they clearly forgot that multi-jumps are possible...if you want them to learn how to play, you remind them. There's no rule that says that once the game has begun, everyone must muddle through on their own.
Learning D&D is a process...and knowing how much to help with that process depends on your players. As a DM who has run for a lot of new players, I routinely have to remind my players of all the things their characters can do. Because these are things the character should know but the player does not.
Your concern that this strips away player agency is not something you need to worry about. You are not mandating that they do something, you are not taking away their choices. You are simply pointing out that another option exists.
So, here is what I recommend.
Ask them if they'd like input from you.
Go with something like...
If they say yes, a simple "Hey, just in case you forgot, your character can cast Mage Hand...which is kind of like short-range telekinesis." or "Hey, just a bit of advice...when you see a bunch of enemies in a clump like that, hitting them with an area of effect spell, like fireball, is usually a good idea."
For more complicated things (such as breaking and entering), I will call for a check that provides a hint right in the call. To give a recent example, the party was looking at this well-secured building, trying to figure out how to get in. So, I said to the party Rogue...
The rogue knows how to break into a building. There's no need for a check to see if they remember how to make locked doors stop being in their way. Instead, I called for a more specific check to determine how good of a job the Rogue did at picking out the specific vulnerabilities of this building.
Even if their check wasn't great...that still plants the idea in the party's head of "what other ways can we break in?"
Checks should be for things that challenge the character, NOT the player
What I would NOT suggest is calling for rolls for your characters to remember what they can do. Just tell them. This is not something their character has to try to remember or struggle to recall. In the example of Mage Hand...that character has cast that spell a vast number of times during their training...remembering that they can cast that spell is not 'challenging' for that character, it's hard for the player. Dice rolls should be about the character, not the Player behind them.
In Summary...
D&D isn't a competitive game...the DM is yet another person who is working with the party in order to make an engaging, fun game. The fact that they run 'the enemy' doesn't matter. You aren't their foe, you aren't trying to beat them. If their lack of experience is getting in the way of them having a good time, then volunteer to help!