Unable to upgrade from 18.04: Sorry, no more upgrades for this system

Solution 1:

You seem to be running a 32-bit version of Ubuntu, as evidenced by:

There will not be any further Ubuntu releases for this system's 
'i386' architecture. 

That's correct. 32-bit desktops have been dropped from future releases, including 20.04. There were simply too few 32-bit desktop contributors and testers.

Your current 32-bit Ubuntu 18.04 will be supported for the full five years (until April 2023).

Ubuntu draws it's strength from volunteer contributors and testers. It's quite possible to resume 32-bit desktop development...if enough volunteers step up to handle the (considerable) work.

If you happen to be running 32-bit Ubuntu on 64-bit hardware, you can install 64-bit Ubuntu. You cannot "upgrade" to the different architecture -- it requires a new install.

Solution 2:

Move your home directory to a different partition.

Make a list of all your installed software.

Shrink your root partition. 32GB is usually enough; 64GB should be plenty.

Make a new root partition elsewhere on the disk.

There are guides to doing all these steps online. Google how.

Install a new clean copy of 20.04.01 in your new root partition. Tell it that /home is your new home partition. Use the same username as before.

After this you can dual boot old 32-bit and new 64-bit systems.