Humans aren't as bad as you think
Firstly, humans gets +1 to all stats, in the PHB (pg. 31):
Ability Score Increase. Your ability scores each increase by 1.
This means, as @SeriousBri pointed out in a comment (now deleted), they can get higher starting stats when using the point buy system. But even with rolling for stats, if you end up with a bunch of odd numbers, this can increase all of the modifiers by one.
(To quote a player at an RPG club I go to, after rolling either mostly or entirely odd numbers: "Well... looks like I'll be going human!")
Secondly, the variant human rules (which I believe is AL-legal, as far as RAW goes). They get +1 to two stats, plus a free skill proficiency, plus a feat. This last point makes them very strong (depending on what feat you're going for).
From the PHB again, page 31:
Variant Human
If your campaign uses the optional feat rules from the Player’s Handbook, your Dungeon Master might allow these variant traits, all of which replace the human’s Ability Score Increase trait.
Ability Score Increase. Two different ability scores of your choice increase by 1.
Skills. You gain proficiency in one skill of your choice.
Feat. You gain one feat of your choice.
As an example, making a Barbarian or Paladin or something who uses a great weapon, you can pick the Great Weapon Master feat, which allows a second attack (as a bonus action) if you crit or kill something. This is essentially Extra Attack at level 1, which is very strong.
Furthermore, it's possible for a human using the variant rules to have a 20 in a stat at level 1. As an example, elves get +2 to Dexterity, so if they roll an 18, they can have a 20 in Dexterity at level 1. However, recently a player in a game I'm playing in rolled an 18 as a human wizard, put that in Intelligence, used one of their "+1 to any two stats" to make that a 19, then took the Linguist feat (which, among other things, gives +1 to Intelligence) to increase that to 20.
Ok, so they don't have darkvision, but neither do Dragonborn or Halflings.
Simply allowing more arms is overpowered
Allowing a PC to use a two-handed weapon with a shield is overpowered indeed. The game wasn't created with that in mind: either your character use a two-handed weapon to deal more damage or use a shield with a one-handed weapon, trading-off the higher damage for better protection.
By simply allowing a PC to have four-arms, without limiting what it can do with those will surely break the game. The PC will be able to ignore a lot of "exclusive options", trade-offs it can simply avoid; the two-handed weapon with a shield is just one of them.
Spellcasting with a sword and shield (without War Caster), wielding a shield with a spellcasting focus and dual-wielding, using a hand crossbow with an shield, and any other situations that can't happen when you only have two arms are some of the trade-offs a four-armed creature can avoid.
So, how to balance it?
If I were to create a Thri-Kreen race, I would limit what it can do with those extra arms. A good starting point is to limit what interactions can be done with those extra arms. The Trunk feature from the Loxodon (Guildmaster's Guide to Ravnica, page 18) gives us a good starting point:
You can grasp things with your trunk, and you can use it as a snorkel. It has a reach of 5 feet, and it can lift a number of pounds equal to five times your Strength score. You can use it to do the following simple tasks: lift, drop, hold, push, or pull an object or a creature; open or close a door or a container; grapple someone; or make an unarmed strike. Your DM might allow other simple tasks to be added to that list of options.
Your trunk can't wield weapons or shields or do anything that requires manual precision, such as using tools or magic items or performing the somatic components of a spell.
Of course, the thri-kreen extra arms aren't like a trunk, so it needs tweaking. I would reduce the number of pounds it can lift, and well, a thri-kreen can't use arms as a snorkel. I would also remove its ability to grapple or interact with a creature; their extra hands are small. Instead, I would allow them to have "one additional interaction with an object or environment, for free, during your turns".
The most important limitations of extra arms are in the second paragraph. I would never touch those, because that's where the majority of problems lies with extra hands.
As Matthieu M. pointed out in the comments, a good explanation for why shouldn't a Thri-kreen extra arms be limited, is that the creature's brain is limited, and can't coordinate so many tasks with the required precision.
Best Answer
The Thri-Kreen in the Monsters Manual (page 288) have four arms. The benefit they seem to gain from this is the ability to use a two-handed weapon while wielding another weapon.
Without houseruling anything, a creature with extra hands would just get more hands wherever the rules call for hands. For example, a weapon with the Two-Handed property "requires two hands to use", so you could potentially wield two of those (although, depending on the configuration of the arms, this may not make any physical sense). Grappling and some spellcasting require a character to have a "free hand". A four-handed character would have a free hand even while wielding a two-handed weapon, or even two light weapons and a shield. In fact, it's perfectly within RAW for a Thri-Kreen to grapple an enemy using its free hands while wielding a two-handed polearm.
An obvious question is whether the character would be able to wield four weapons and make four attacks. RAW says no. The rule on Two-Weapon Fighting would still apply as written, and both weapons need to have the Light property, unless you have the Dual Wielder feat.
This rule from the Dual Wielder feat becomes interesting:
Does that mean you need to wield melee weapons in all of your hands to gain the benefit? As written, it's not clear, but from context (it's dual wielding after all), you'd just need to have weapons in at least two of your hands. The intent is likely that you gain the benefit because you cannot use a shield, so perhaps the rule should be that you have a weapon in two hands and no shield.