Gog.com, Mods, Steam

I bought project hospital on gog.com, does anyone know how can I download my steam mods in my game

If you're asking whether you can use mods on a GOG version of the game, it depends whether each mod dev has made it available. There are a few on Nexus and then others have external download links from their respective Steam or Discord page Hope that answers your question.

I know this is late, but I also bought through GOG and just found out there is a website to pull workshop mods from! Use this:

steamworkshopdownloader(dot)io

Note: Since I am a new user (I made this account so that I could answer your question), I can't paste in external links for 7 days. So, replace the "(dot)" with an actual "."

Edit:
I just found it out from the dev themselves! You extract to:
\Assets\StreamingAssets\Addons