After SERVER-105573 all search stages will fail when run on a timeseries collection. However adding support for $listSearchIndexes was difficult. Currently, $listSearchIndexes runs on the host to which the request was originally sent. In other words, mongos will not forward the command to the shards. However, if the collection is untracked on a sharded cluster, mongos must forward the request the shards to check if the collection is a timeseries collection. However we want $listSearchIndexes to only run once. It is not trivial for mongos to forward the commands to the shards, but only run the stage once.

This ticket should investigate the fix, and if it's too difficult we can keep the current behavior ($listSearchIndexes will return an empty list for timeseries collections).