Did you claim it yet? For the first run, you should run it directly from the command line using something like:
node /path/to/plexamp/js/index.js
It should direct you to visit https://plex.tv/claim to obtain a claim code and enter. After doing so, you should see a message that Plexamp is signed in and ready, after which it will exit. You can then run it again from the command line or via a systemd service.
This describes the process, but it may be a tad out-of-date (it may not be):
https://forums.plex.tv/t/plexamp-on-the-raspberry-pi/791500
I just set up a new Plexamp headless install a Pop OS VM and it worked as expected.
Note that Plexamp headless requires node.js version 20.x.x (not later). You can find standalone binaries for that version here:
https://nodejs.org/dist/v20.20.2/node-v20.20.2-linux-x64.tar.xz
