How do I make WordPress use a template for any requests where the url is /careers/[0-9]+?

We used to have custom posts for job openings handled by single-jobs.php – then switched to an Applicant Tracking System with a nice REST API, meaning no more job posts in the data base on our end.

I considered making a single job page with an id parameter (bla.com/careers/job?id=123). A page-job.php template would then read the parameter and use to request data from the API and then echo a page accordingly.

But for SEO reasons, I want the routing to have “proper” slugs such as bla.com/careers/123.

Would I need to basically do what I suggested above except use JavaScript to change/fake what the url looks like, or is there a backend way of doing that?

How do I make that happen?