Too Long; Didn't Read: Change "Remote Quality" and "Local Quality" to [ORIGINAL/MAXIMUM] in Plex client settings.
For some stupid reason, plex defaults to 720p when you first set up a streaming client (Smart TV apps, Apple TV, Roku Sticks, Chromecast, etc). This not only gives you a lower quality stream, but also puts stress on the server because it has to transcode down to that quality.
Click the device you use to stream for instructions.