How can I save text messages from my iPhone 12 onto a PC?

It is not possible to transfer your SMS messages directly to your PC. You need a Mac, or a 3rd Party program for Windows.

Programs like, AnyTrans claim that they can transfer SMS messages from your iPhone to PC. However, the program is not free. Do a Google search for Transfer iPhone SMS to PC - there will be lots of results.

It's simpler on a Mac. If you have access to a Mac, with your Apple ID and messages on, then it may be possible to export the messages as a PDF.

On your Mac, open the Messages app and find the conversation. Tap File, and then Print. A new window appears, at the bottom is "PDF" in a drop down menu, expand the menu and select "Save as PDF”

Unfortunately, the iPad does not have this option.

In MacOS you have the option to print out your messages. It is in this process that you have the option to save the entire printout as a PDF file.