Hello!

I was recently looking on the GOG Connect program as I wanted to import Paper's Please which I bought from Steam onto my GOG account however whenever I refresh it, Paper's Please isn't showing in my available or unavailable games.

My Steam account is Public and its also not showing Prison Architect.

Can anybody help?

Sometimes you just need to wait a day until the program is able to register your games properly. Especially if you just changed your Steam profile's privacy settings to public it may take some time.
However I also had it once with one game that simply won't get registered by GoG Connect although it was listed, while my other games in the list got registered. If you really want the game to get registered I suggest to contact the GoG support right when that happens. - I guess they aren't able to find the problem just yet, since it has been some time.