Investigate MR homepage timeouts when users have too many MRs

Summary

Original report: #512419 (comment 2763955373)

Users with a large number of merge requests experience 503 database timeout errors when accessing the merge request homepage, resulting in no merge requests being displayed despite having a non-zero count.

Logs: https://log.gprd.gitlab.net/app/r/s/TLlfE

Goal

1. Investigate the query performance threshold - at what number of MRs does the timeout occur?
2. Identify how many users might be affected by this threshold - whether they've visited the MR homepage or not