No it has always been an additional purchase. The only "self driving" mode that's included by default is their "auto pilot", which is just TACC with better lane assist so it can take sharper bends in the road without "bouncing" between the lines like most other cars do with lane assist.
Most people seem to incorrectly think that autopilot and FSD are the same thing, but they are not.
They distinctly labeled them with names that are not even remotely close in wording, one even with a very clear and precise name of the intended feature set (FSD). I can't really see how people can think they're the same TBH, especially considering the clear distinction between the two on their website.
I 100% agree the feature set of FSD is false marketing and wildy misleading as it's currently not even close to delivering anything beyond level 2 autonomy, and hasn't for the past decade since they announced it was "ready end of year", albeit still more capable than the auto pilot feature (at least in the closed beta).