We also encountered this issue, and my predecessors constantly increased the link limit for a decade. However, this comes at a price and will eventually cause significant performance issues.

Our problem was related to a Shared Step in almost all test cases. We plan to retire this shared step by either recreating/renaming the old one "(archived 2024)" or manually typing the steps into the new/affected test cases we are copying.

How we found the heavy link shared steps:

1. Create/run a query (under board>queries)
2. Set the parameters: Work Item Type=Shared Steps AND State=[Any]
3. On the toolbar, click the "Column Options" button
4. Add the column "Related Link Count"
5. Under sorting, add the column "Related Link Count" and order by descending
6. Run the report and fix the affected test cases

Steps 1 2 3 6

If you don't have the same issue with shared steps, you can likely use the same process to check other work item types.