Low quality on remote access

Plex Documentation
Remote Access
Troubleshooting Remote Access

Plex ForumsTips, Tricks & How-Tos
The Basics of Remote Access Troubleshooting

If remote access is not working, Plex will fall back to Plex Relay, where the stream is tunneled through servers at Plex and limited to 1 Mbps (2 Mbps w/ a Plex Pass).

You can monitor playback via Plex Dashboard → Now Playing. If the connection is Indirect (versus Local or Remote), then it is using Plex Relay.

See the documents linked above for details on configuring and troubleshooting remote access.