I bought TBOI Rebirth at Steam a pair of months ago but now it's at GOG and my question is if I can play all the game if Rebirth is at my Steam library and the DLCs are at GOG

I think you can't buy the DLCs alone, if you don't have the base game they can only be bought as gifts for other people.
AFAIK you can't even buy dlcs alone on steam

Steam just got a new update (version 1.7.9) with multiple changes and fixes.
Changelog is here:
https://store.steampowered.com/news/app/250900/view/3409815046669797018

Hopefully, we'll see this update on GOG too in the next few days --and not have to wait for months again.

Apparently there are some exciting dailies also going on, according to the changelog post above, but GOG does not get the daily challenges so no luck there.

Steam's version just got another update (1.7.9b, Dec 8, 2022) . Changelog is here:
https://store.steampowered.com/news/app/250900/view/3645131352093069363

This is the second update since 1.7.9 release (on Steam), as the previous was 1.7.9a (Nov 11, 2022) with changelog here:
https://store.steampowered.com/news/app/250900/view/6232446836692812577

As of yet GOG's version still remains 1.7.8a (March 2022) with no info on ETA for the update -- or any feedback about how to unlock items that are connected to daily achievements which are missing from GOG.

Seems we're still stuck with "v1.7.8" version, missing last updates and new language support, more than 3 months after its steam release (04/11/2022)

I regretted leaving a 1 star review once they FINALLY updated the game last year, but since it's sorely outdated once again I guess it's still appropriate!