When looking at recently verified runs (example: https://www.speedrun.com/api/v1/runs?status=verified&orderby=verify-date&direction=desc), is it possible to embed what the run's rank is? I'm trying to minimize the number of API calls I need to make (because throttling).

Unfortunately no. Run data on its own has no concept of rank, since there are a lot of things other than just the run itself required to define that. Only the leaderboard endpoint can give you rankings.

Unfortunately no. Run data on its own has no concept of rank, since there are a lot of things other than just the run itself required to define that. Only the leaderboard endpoint can give you rankings.

That point seems tenuous to me since SRC itself displays a ranking of sorts outside of leaderboards frequently, such as on player PB pages https://www.speedrun.com/user/dadinfinitum or on a run page itself https://www.speedrun.com/sml2/run/zq6w2x1y if its on a leaderboard.

As for a solution, you may be able to use my API https://sr-browser.dbeal.dev/api/v1/runs/zq6w2x1y based on the code from my middleware https://github.com/dl00/speedrun-browser-middleware/

That point seems tenuous to me since SRC itself displays a ranking of sorts outside of leaderboards frequently

That is why I thought it should be available. Using leaderboards isn't the end of the world, though.