M2 Macbook Air refuses to work with my Samsung SCX-4500W Printer

Bad news first: macOS incorporates native support only for AirPrint enabled printers and multifunction devices and the Samsung SCX-4500W is not among them. Generally speaking if you need to download a driver for a printer, then that printer isn't going to work.

There is a small sliver of hope. When you set up that new Mac, did you transfer its content from the Intel Mac? If you did not, consider erasing the new one and setting it up again. Since it's new, you have nothing to lose. This time, when asked to transfer information from another Mac or its Time Machine backup, choose that option.

That — may — transfer the older one's existing drivers and put them in the correct locations in the new Mac. Apple has sealed off third party access to those locations in recent macOS versions, but in many cases existing drivers were considered "grandfathered" and are permitted to remain in place. An "upgrade installation" or "transfer from another Mac" kept them operational, whereas a brand new Mac will generally prohibit the installation of legacy drivers.

Other than that improbable solution, the very unattractive workaround would be to relegate that older Mac to act as an overpriced printer server as you did. That will work.

I´ve been struggling with a similar problem trying to print from a Mac Mini M1 with OS Ventura. It doesn´t work, but it works if I let my old MacBook Pro from 2009 share the printer via Bonjour!