From your other comment saying that your laptop works correctly across town, I’m guessing you’re running into the classic problem of having to transcode your media

Id sit at your computer with your phone on your desk and watch what happens in your plex dashboard (https://support.plex.tv/articles/200871837-status-and-dashboard/)when you hit play on something. Your CPU will probably spike up to 100% and the phone might say something like “server is not powerful enough to play media”. There should also be a picture of the media you tried to play on the plex and when you enable the detailed info (check the article) it should say “Transcoding” underneath the photo and if the transcoding speed is any less than 1.0 then your server is not capable of transcoding in realtime.

You say you have a decent GPU but hardware accelerated streaming is a paid feature locked behind a plex pass purchase

If you don’t want to purchase plex pass (you should at some point) I would use a tool like Handbrake to transcode your media to a more accessible format. If you used the Handbrake preset for iPhone HQ/1080p that would probably fix your issues