How can I find a team that's more on the stable side?

You mentioned it in your question, and I think it's valid: Work on ads.

At the end of the day, ads is the bread and butter of Meta and will remain that way for at least the next 5 years, probably 10. I know that Zuck is really bullish on the Metaverse, but I think there's a 50% chance he cans it under increasing market pressure and lack of traction.

I think with questions, you can ask some of the things you mentioned:

1. How have re-orgs been historically and what are the plans for future re-orgs?
2. What business impact has the team delivered in the past year? What are the plans for the next year?

That being said, finding a stable org in Meta is almost impossible from my experience. If the org is doing well, it will grow and re-org. If the org is doing poorly, it will shrink or get canned. It's also dependent on exec quality (bad VPs/Directors will do bad re-orgs), and it will be hard for you to gauge that as an E5 (but you can ask around regardless). And in this climate, I imagine there's going to be a lot of turnover at Meta due to poor morale, which will lead to re-orgs as managers/execs leave. Temper your expectations here.

Lastly, I recommend this video on finding a team with good growth opportunities.