I've had this chat bug for almost a half a year now but GOG doesn't seem to do anything about it despite been in contact with the support two or three times since the bug appeared. I have this exclamation mark with (1) message above the chat section all the time and i seem not to get rid of it no matter what i do. I got fooled in the beginning when i always thought i got a message from someone but it turned out there weren't sent from anyone.

Strange thing is people seem to get added to the chat section even though i have never spoken with them.

This is not a Gog Galaxy issue and it appears on the site as well. What should i do? Do i really have to report it to the bug tracker?

Probably you got a pm from scammer which account was deleted..
I'd contact supprt if I was you.

I have the same bug

I already contacted support many months ago but they have not resolved my problem yet.

Must have been a very difficult problem to resolve ;-) but it's supposed to be fixed now:
See here: