I take it you’re trying to download media from your own server (e.g. no movies from Plex’ video-on-demand service or other online media sources)?
From what app are you trying to download the items? Downloads are only supported on the mobile clients (Plex for Android / iOS) and the Plex for Mac/Windows/Linux desktop app.
As shown in @SE56’s first screenshot, the web app has a “Download File” entry from the 3 dots menu. I’ve never used this but I assume it gets you a copy of the file to then double click and play when offline.
Can you try signing out on those apps and back in to see if the issue persists.
If it persists, try signing out of the server and back in (Settings > [Server Name] > General > Sign Out)
open the server locally (using its local IP or http://127.0.0.1:32400/web if you’re on the same machine; then go to Settings > [Server Name] > General → same place from where you signed out)
You can download media hosted on your own Plex Media Server or media from libraries shared with you by friends (if they give you permission to download).
Did remote access work for you before?
Remote access can be tricky because there’s so many players involved. Common troubleshooting steps are documented here → The Basics of Remote Access Troubleshooting
To the best of my knowledge, Plex doesn’t advertise an option to download media from their online media sources. IIRC this is due to licensing limitations.