How to manually update?
Being connected to the internet is one step, next is
softwareupdate --all --install

Should that fail, I would test APNS notifications to see if your network may be blocking outbound and inbound traffic to Apple servers.

https://twocanoes.com/products/mac/push-diagnostics/
https://support.apple.com/en-us/HT210060

The second link explains what network ranges and ports have to be free of interference. One typical situation is a network is performing one of MITM attack / HTTPS Interception / SSL Inspection of the traffic between your device and Apple, rendering the secure connections invalid.
This can also just result from Apple services are in an error condition or your network or OS has issues. I test that with a command line invocation if the software update tool.
You can then run the full installer to accomplish your update or see errors why it’s not progressing in many cases.