Exactly what patches, offiicial or otherwise, are included with the GOG version?

Official patches 1 and 2. Probably some 3rd party dll fix for compat sake.
Why?

It's been years since I've played, and I know there are various unoffical patches and mods. I just don't want to install something that might already be included.

I plan on using the CO8 mod but without the extra content. Is that the only thing I need to install if I want bugfixes while keeping the game as vanilla as possible?

The CO8 installation guide accounts for the GOG version, read it carefully:
https://co8.org/community/threads/circle-of-eight-modpack-installation-instructions.6695/

Tldr install Co8 and play through Temple+ Well it was pretty obv you're asking bc of smth like this but then your q should be diff and probably asked in google its been covered many times. On this very subforum very recently too. You can't.

You could play the new content edition for all that matters. It won't get in your way much during the course of the original campaign. I mena much more than the new content thats already there... In the no new content edition)
The bulk of this NC is after the orig endgame. You could at least mention that this stuff is 7 yrs old and much of the DOs and Donts there are outdated due to the T+ fixes.
At least we can use our (quick|auto)saves now safely)))
PS ah, its a diff howto. I was thinking about the one which says don't quicksave, don't do this or that. Point stands tho. And this one is a bit too detailed, you just install java, Co8 and activate - job done (regarding the Co8 pack that is)

Cool story.

yeah, you Q was dumb. chill.

Your trolling is dumb

You can compare various versions of the game here.
'CD Version + Patch 1 & 2 + TemplePlus' is the way to go, according to the author.
The GoG version is, admittedly, a modded version but it's mostly bugfixes and a few spells added. (you can find the changelog in the moebius zipfile)
For a close enough vanilla experience I'd pick the easy route and go for 'GoG + TemplePlus' unless you're a reviewer.

I advise against making decisions based on this debatable and sometimes outright dodgy and dubious write up (content wise - nevermind the wonky layout and broken navigation).
Largely a fanboy's wishful thinking and a pipe dream.

In case you want some reality check on how wretched the development of ToEE was, I'd point you here https://www.rpgwatch.com/forums/showthread.php?t=44764&page=4
no wonder it came out the way it had. lots of what relayed there from the horses mouth is guessable just from playing the game.