More detail than you probably need, but here goes anyway.
If the music files are on an internal drive on the old PC, then you need to move the files. If they are on a external usb drive, then you can just move the external drive to the new PC. I am assuming they are probably on an internal PC.
The music files probably do not have all the tags in them that MC uses. MC stores the tags and cover art it uses in a separate library, independent of the actual music files. The library also contains any setup options you have made on the existing copy of MC. You need to transfer that library data to the new machine. To do that, you need to do a backup of the library on the new machine (File - Library - Backup), then move that library file to the new PC and Restore it with the new version of MC. A MC 20 backup should restore to a new MC 23, but there is a chance it will not. Let's assume it will for now. But you need to move the music files first.
There are two ways to move files. One is to use the Rename, Move, Copy tool within MC. To do that you need to connect both systems to a network and allow the old PC to have read/write access to the new PC's drives. The second way to move the files is just using Explorer, either across the network or using a portable usb drive as a intermediary.
To move the files from the old PC to the new one with Explorer, the easiest way is to do it via a network. You just have to connect both PCs to a local network and give the new PC read access to the files on the old PC. Then you can use Explorer to copy the files from the old PC to the new PC, duplicating the new file structure exactly. That is, if your files are stored in c:\music on the old PC, put then in c:\music on the new PC exactly as they are on the old one.
If you do not know how to set up a network to do this, then you can copy the files from the old PC to a usb drive, then move the usb drive to the new computer and copy then to the internal drive on the new PC. Again, you need to duplicate the file structure exactly.
Once you have the files on the new PC in exactly the same directory structure, you can Restore the library (File - Library - Restore) and everything should pretty much work.
The Rename, Move, Copy tool is very powerful and can be used to move the music files. If you use it, just take it slowly. It is easy to make a mistake at first. So, a trial with a few files is easy. In this case, you probably want to do a copy, keeping the music files and library on the old PC in tact while creating new ones on the new PC. Again, you want to exactly duplicate the file structure on the new PC.
Once you install MC 23, it will start to do an auto import. You should stop that. That will allow you to restore the copy of the original library.
If you want to use the old PC to play the files stored on the new PC should should look at the Media Network options for setting up a client/server solution. That would let you use the existing music plus any music you add. You would have to upgrade the version of MC on the old PC to do that. The MC23 license can be added to both machines. There is no extra charge for the second license.
I am sure you are aware of this, but do not delete anything on the old PC until you are completely satisfied with how the new one is working.
Good luck.