As this was never answered... This is a feature I would love the Google Search Console API to provide but unfortunately it does not. I doubt very much it ever will (in case you hadn't guessed). You can get a sample of internal links for a given URL using the URL Inspection API (launched in 2022) but it's simply a sample and a rather arbitrary one at that so entirely useless in my opinion.

For link metrics you will need to use Ahrefs, Majestic, SEMrush (for backlinks) and a crawling solution for internal link numbers.