Can a PC of the thri-kreen race make a bonus action attack through two weapon fighting? Example: A thri-kreen fighter holding a shield and scimitar in their main hands, and a dagger in their smaller hands. If this character attacks with their scimitar and then use their dagger to make an attack as a bonus action as per Two-Weapon fighting?
Yes, but only with a light weapon
In the Astral Adventurer’s Guide for Spelljammer: Adventures in Space, the Thri-kreen racial trait Secondary Arms says (emphasis mine):
You have two slightly smaller secondary arms below your primary pair of arms. The secondary arms can manipulate an object, open or close a door or container, pick up or set down a Tiny object, or wield a weapon that has the light property.
Since this is the only info about what the arms are capable of, this is everything they can do. While it doesn’t specifically say they can be used to attack, it does say they can “wield” a light weapon.
Wielding a weapon is different to just holding one. “Wield” doesn’t have a defined game meaning, but is consistently used in Dungeons & Dragons with its general English meaning: “to hold and use” something, usually a weapon (though also sometimes another item like a shield or wand, or metaphorically “holding” but literally using magic). So the secondary arms can hold and use a light weapon.
That makes it possible for a Thri-kreen to wield a scimitar, a shield and, in their secondary hands, a dagger as you describe.
They could also make a two-weapon fighting offhand attack as a bonus action with the dagger, as long as they are fulfilling the other requirements of two-weapon fighting. Those rules refer to the two hands holding weapons as “one hand” and “the other hand”, but they don’t say anything about those hands having to be the only ones the character has!
Note that if the character gains a feature such as the Dual Wielder feat that allows them to use larger weapons for two-weapon fighting, they will still only be able to use a light weapon with their secondary arms. The feat doesn’t alter the abilities of the secondary arms.