Is this the same version that's been on Steam (censored) or is it the full uncensored version?

Hi,

I assume you mean the first game, cause AFAIK there was no censorship done for the second game in any release (I hope I'm right).

For the first game's censorship, check this out - https://steamsplay.com/yesterday-if-youre-bothered-with-censorship-and-or-audio-glitch/

Note that this solution is for the Steam release, but I see no reason why it wouldn't work for the GOG release as well (if the GOG release is indeed censored, I have the first game on disc so I wouldn't know)