Flaky test: `TestAlertmanager_StateReplicationWithSharding_InitialSyncFromPeers`

[pstibrany]

--- FAIL: TestAlertmanager_StateReplicationWithSharding_InitialSyncFromPeers (3.88s)
    --- FAIL: TestAlertmanager_StateReplicationWithSharding_InitialSyncFromPeers/RF_=_2 (1.49s)
        multitenant_test.go:1617: 
            	Error Trace:	multitenant_test.go:1617
            	Error:      	Not equal: 
            	            	expected: 1
            	            	actual  : 0
            	Test:       	TestAlertmanager_StateReplicationWithSharding_InitialSyncFromPeers/RF_=_2
FAIL

[pracucci]

@stevesg Could you look at it, please?

[pstibrany]

Still flaky :(

https://github.com/cortexproject/cortex/pull/4302/checks?check_run_id=2875590548