The test (jstests/sharding/timeseries_multiple_mongos.js) was first introduced in SERVER-60144 with the intent to ensure StaleRoutingInfo were correctly handled in case of sharded timeseries. 
However, the test seems to be gone further beyond that scope and it's currently testing specifically the amount of interactions a specific shard and the router will have in case of both stale sharded and unsharded collection.

For every operation, it checks a specific shard is reached specifically N times. 

After SERVER-83878 with the introduction of the unsplittable timeseries collection the sharding protocol never changed, but amount of request did. 

The test is broken even though we don't have specifically any bug. The test should be rewritten to test that in case of stale mongos the command simply works.