Can’t explain what is in the video. I’ve only seen that happen when (a) the web browser will not let Plex set cookies, or (b) the web browser clears cookies.
My Mac is circa 2011, but I do not see that happening using either Safari or Chrome.
Regarding the Plex desktop client, suggest you take another look (download). It has the same layout as Plex Web, but is more full featured. It does not have the limitations imposed by web browsers and direct plays most audio/video codecs.
If your Mac has an AMD GPU, you need to edit the plex.ini file to make sure the app launches correctly. See this post for details: Plex for Mac - Player v. 1.44.0 - 1.45.0: Grey Screen on Startup (MacPro6,1 & 7,1) - #24 by BigWheel
