Commit e545dedf72bff2bd41c93c93eb576929fce37112 moved `TransactionAddedToMempool` to the background scheduler thread. Thus, adding a transaction to the mempool will no longer add it to the wallet immediately. Functional tests, that `sync_mempools` and then call into wallet rpcs will race against the scheduler thread.

Fix that race by flushing the scheduler queue.

Fixes #12205; Fixes #12171;
References #9584;