I noticed that I can't run PoE 2 if GOG Galaxy is not running. I've tried to call the game directly from the executable in the folder, it starts, shows the "Obsidian" logo and then return to the Desktop. Then, I start GOG Galaxy, run the same executable and the game runs.

Anyone else noticed this issue?

I noticed this, but I installed POE2 using GOG Galaxy, which adds a bunch of hooks into Galaxy for tracking achievement, playtime, etc. Those hooks don't exist unless the galaxy client is running and logged in.

I expect that if you install it using the backup installer, you wouldn't experience this problem, though I haven't tried that with this specific game.