It is a process known as ceremorphosis.
Several articles about the Baldur's Gate III trailer indicate that the depicted process is indeed ceremorphosis.
Rock Paper Shotgun touches on it:
They call it Ceremorphosis. The excruciating seven day process by which a humanoid might transform into a Mind Flayer. Stick one illithid tadpole in the brain and one week later you’ve got an octopus for a head and a craving for more grey matter. [...]
Before we chat specifics: that reveal! Blimey. Ceremorphosis might be the inspiration, but when crafting a 90 second teaser trailer you’ve got step on the gas a bit, so the process is accelerated. A week of suffering becomes a frankly horrendous slice of Cronenbergian body-shattering that is so gnarly the uncut version of the teaser was not shown at today’s Stadia announcement. I know Google want us to give their streaming tech a thumbs up, but not when that thumb is being snapped 90 degrees by a mind maggot.
It's confirmed by the devs themselves in this GameSpot article, in an interview with Larian Studios head Swen Vincke:
For anyone who's not familiar with Baldur's Gate, as you said before there are people that are new to this franchise, can you kind of break down what we're seeing in the teaser that will catch us up and get us ready for Baldur's Gate 3?
[...] There's dead bodies everywhere and then something's happening to this knight and he's actually undergoing a version of what we would call accelerated ceremorphosis, which is basically a way of reproduction that these creatures called the mind flayers have.
They stick a tadpole in people's heads, that tadpole grows, and then it turns a human being or any humanoid being into a mind flayers and these are the guys you may know from Stranger Things, maybe. They're these psyonic creatures with tentacles and very intelligent but they're hive creatures. They have elder brains that command them.
They used to have an incredible empire called the Mind Flayer Empire but things went wrong, so they've been in hiding ever since in a place called The Underdark, which is like the deep underground of this world of Forgotten Realms. Somehow, they've managed to get people into Baldur's Gate that are turning into mind flayers and you see some shots where they're flying in the distance, so it's an invasion of mind flayers, too.
You can find more information about the process in the Forgotten Realms wiki article on ceremorphosis, which cites books from past editions as well as Volo's Guide to Monsters.
Larian Studios co-founder Swen Vincke also jokingly recreates the meeting with Mike Mearls and Nathan Stewart in the first Community Update video by Larian Studios for Baldur's Gate 3. In it, they do discuss the process of ceremorphosis.