[lib] Fix stack overflow from lastUpdatedTime

Summary: This resolves ENG-10016. It looks like when this was changed from an immediately-invoked Promise to a function that returns a Promise, we ended up in a situation where the lastUpdatedTime dereference ended up resolving to the new value rather than the prior value.

Test Plan: Prior to this change, I was able to reproduce the issue in the Linear task. Afterwards, it no longer reproduces

Reviewers: tomek, angelika, varun, will

Reviewed By: will

Differential Revision: https://phab.comm.dev/D14156