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Will this game has that feature? Copying manually my progress beetwin stationary PC and GPD Win is a little bit annoying.
Are you sure you're talking about GOG Connect? Because Connect is an occasional "promo" GOG does, allowing people to redeem copies of games they own on Steam over here.

I assume you're talking about cloud saves. Sadly, Enter the Gungeon doesn't support cloud saves on GOG Galaxy (yet?). Maybe some time later?