Migration from PE12 to Lightroom

Classical process:

1 - You install another instance of your PE12 on the new computer (or better a trial version of the current PSE 2022, free for 30 days)

2 - From that new PSE2022, you restore everything where you want in the new computer where you want in default or custom location. If necessary, the organizer catalog conversion to version 2022 is automatic

3 - You use Lightroom to convert the organizer catalog to the Lightroom format.

https://community.adobe.com/t5/lightroom-classic-discussions/moving-from-pse-14-on-one-pc-to-lightroom-on-new-pc/td-p/8805823

Tips:

If you choose to store your restored library on an external drive in custom location, you should not need to install another PSE version. Lightroom should convert the catalog found in the external drive.

If you choose to reinstall PSE12 on the new computer, beware of the number of available activations; if necessary, deactivate one of the two allowed activations before reinstalling. Or download the current PSE2022 trial version.

With a PSE organizer version on the new computer, you can access your photo files like before as well as from LR. Be careful not to use both softwares to organize: what is made in one is ignored by the other.