From what I see on local clients, roughly in this order:
1. Mentions on other sites. Reviews, directories, list articles, Reddit threads. AI answers lean a lot on what third parties say about you, not just your own pages.
2. Consistent entity info everywhere. Same name, address, phone, categories on GBP, directories and your site.
3. Pages that answer the question directly in the first lines, then explain. FAQ style sections get quoted a lot.
4. For local, Google Business Profile reviews and how recent they are.
5. Being crawlable at all. Plain HTML that loads without heavy JS, AI bots not blocked in robots.txt, basic schema.
Classic backlinks still matter but less than people think for this.