it seems like clicking entries in the dropdown might do anything except what you expect.

Its not clear when you are clicking, are you complaining about having to wait for Synapse to echo the change down Sync? https://github.com/vector-im/riot-web/issues/14280
oh nvm wtf
I think this is the perf stuff gone wrong
Can you be more specific about "gone wrong"? It still looks like local echo to me.
It is related to local echo, the Room Tile doesn't update once that echo comes down, it doesn't react to push rule updates
(so effectively it lags a click behind)
Best solution to this (without causing a performance regression) is https://github.com/vector-im/riot-web/issues/14280
Considering this a duplicate of https://github.com/vector-im/riot-web/issues/14280 for tracking purposes.