Final update for this post!
The reason why I was getting this message:
Server list query returned an error: System.Net.Http.HttpRequestException: Response status code does not indicate success: 521 (). <- System.Exception: Could not query via https://play.example.com/ - check if your sv_listingHostOverride is correct
Is because I blocked all requests coming to the server, after properly setting up the firewall settings everything works correctly.
No more issues with proxy, no more issues with the play. subdomain.
In the end, I ended up migrating the FiveM server to a Windows box instead of running it on Linux. You can set up nginx as a service on the Windows box if you want to, but I recommend running a separate nginx server that proxies to your game server.
I’m still using these settings and everything is working.