Converting a themes featured image to WordPress featured image

Migrating from one to another isn’t that complicated usually. As long as you have the logic you can write code to make it happen and run in bulk or tie it to every time featured image is requested for gradual change over.

The bigger issue I see there is that you say images are stored as URLs. WordPress generally manipulates attachment IDs for this, including featured images. URLs are just too inconvenient to work with for many related purposes.

While going from ID to URL is trivial, going from URL to ID is huge pain in general case. Arbitrary URLs might not even be local attachments. You could see my answer on going from URL to ID for a starting point.

Overall without knowing more of your context it is hard to advise on specific approach. If getting to native UI is priority then bulk thorough migration is probably in order. If older posts just need to work sometimes it is easier to just leave them alone with legacy code and move on to new workflow for the current stuff.