Question about package updates

Greeting all. I have been using my omnia for many years now, and admittedly it is getting a bit old.

Recently, I have not been getting package updates at all. As least not as a often as I am used to , and I am starting to think something may be wrong on my side of things. Is there anyway I can check that the update server is able to communicate with my router?

Yes, you have following options:

If you just want to try and see whether the connection is ok, you can again go either

Recently I had the same issue. In my case, changing the DNS provider (e.g. to cz.nic, see Guide - Turris Documentation) helped.
After the update, I changed the DNS provider back to the original setting without issues.

The current stable release is version 6.4.4. It is true that the pace of updates has slowed down considerably compared to earlier times, but they are coming steadily, just slower. There should be a 6.5 release in a while (it has been in testing since December).