Hello!
Thank you!

I did manage to get it run by the work that you guys said here so thanks for the help.

That's what I've done, and I think its fixed now.
1) Start to get the offline installer form Gog.com
after it finishes set up, press exit on the setup window.
2) Cancel the update command on the Gog Galaxy (cancel the updating program on the game list),
3) After going to option of setup, >Manage installation> Configure> Auto update >off >and then check if you see 9 years ago >press that check box<
4) Now press >Manage installation > Verify Repair.
5) Now press >Manage installation> Configure> Auto updates> Repress it ON.
6) Check for update in the menu. And now this should work with all the program update properly. Fingers crossed!
I wish that helped some other Monkey Island lovers.
Have a Good Day! And good Holly Days! Cheers.

I was having the same issue, installation fails at 95% and keeps retrying on a loop, uninstalling also fails and the repair option stays greyed out, so all you can do i close the launcher, manually delete the game folder and reinstall using the offline executable as others have directed before. Is good there's a workaround for this issue, but hopefully this will get resolved because is obviously not ideal, I feel like we are back at the pregog days when we had to perform voodoo magic to make old games work.

It worked.
following arker21's instructions made the game work on my Win11 (version 23H2) via Galaxy.
- Using the offline installer did work normally without Galaxy.

Did not work for me.
I install it with the offline installer, repair 2008++, start GoGalaxy, it immediately starts updating, and it corrupts I bett hat 2008++ again, and it never complets the install, nor allows an uninstall from Galaxy.
Cancelling the update doesn't help either.

The game is still playable though.

this worked for me on Win 10 too.