I would try a couple other things, to first eliminate the conditions.
First, how about pulling from a specific connector? Navigate to the version of the package you want, like /feeds/feed-name/adobereader/2020.006.20042, and then click "Pull to ProGet". That way you'll get a specific connector and a specific version.
If the individual packages work, but the "Add Package" route you took doesn't, then perhaps it's some sort of Mono-related bug. Those are hard to track down, and they come/go as the mono docker image is patched. We will eventually address this by moving to a more stable, .NET core version, once it's released by Microsoft.
Try some other packages, to see if they also don't work. If some packages work, but others don't, it's probably related to your gateway/router blocking things that it sees as security risks.
If that still doesn't work, then consider to attach ProGet to a Proxy server, like a Fiddler instance, by going to Admin > Proxy. You can then monitor the outbound traffic.