I finally resolved the issue I was having.
I checked literally everything. Firewall, ports, possibly antivirus, possibly a service causing the issue (had those before). Found nothing.
After I did a fresh install of Plastic SCM on a VM, I found out that in my preferences there was no connection profile.
I can't remember adding a connection profile, as I've only created a repo, check-ins, and sync views, but probably did on a drunken night.
Upon deleting the connection profile, I have no problems connecting to my cloud repos now.
If anyone is having this particular issue and how to find the connection profile: Preferences > Connection Profiles.
I appreciate you replying to my post, Carlos, but in the end it was my connection profile which most likely wasn't added correctly.