Illithids have a combo of lots of detail and not nearly enough and my memory is both a little fuzzy from it being awhile since i researched them and them being in one of my campaigns with different lore so ill try my best. Generally speaking Mindflayers who are not attached to the hive mind and breaking from the elder brain are ones that have embraced magic specifically studying lichdom. They are known as Alhoons and are undead. As for the ones who just break off i dont think there is official lore so just homebrew but im playing a homebrew warlock mindflayer in one of my campaigns and the general idea if that they are not connected to the elder brain because they study and embrace Arcane magic which illithids are not fans of. Basically taking the idea of the alhoon and expanding it to other camps.
The ability to play as a mindflayer though is very unlikely outside of a DM mode. The tadpole doesnt turn you into a mindflayer but your body transforms into that of one. your brain is consumed and the tadpole basically grows into the mindflayer so its a different being all together although with a knowledge of your memories due to consuming it. unless you had some lore that you are a chosen one whose memory and soul was so powerful you could regain control. The party setting would not make sense sadly since its multi player but maybe only characters who are sympathetic, The Vampire would make sense since you are both seen as evil creatures. I would love a kill on sight race though just like DOS2
