PM and PMMs are likely to have different goals when it comes to feedback from users with early access, but I think that both should at the very least seek to understand, "to what degree have we solved the problem for customers that we set out to solve with this feature/product/release?". If you practice jobs-be-done, that question might be better phrased as "is the user able to hire our product for their job-to-be-done? Why or why not".
As for PMM-specific expectations, I would base these on the goal of your alpha/beta, which you should align with PM on upfront. For example:
- Validate Problem-Solution fit
- Uncover and fix issues ahead of GA
- Source reference customers for a marketable moment
- Improve the UX before GA
- Inform positioning and messaging
- Inform pricing and packaging
Lastly, I've never given or been involved in a project where an incentive other than, "get early/exclusive access", was offered. If you're building the right things for your customers, you should have no issue getting users wanting to participate in a beta. In theory. 😅