Plex Web playback gives playback error s1001 (network) on all media

The remote access status indicator jumping to green and then straight to red after a few seconds implies your remote access setup doesn’t work to begin with.
Did you already have a look at the related troubleshooting support article?

https://support.plex.tv/articles/200931138-troubleshooting-remote-access/

There’s also a guide with some more details on how to troubleshoot remote access issues.