release-23.1: persistedsqlstats: de-flake TestSQLStatsPersistedLimitReached #105930
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Backport 1/1 commits from #105917 on behalf of @zachlite.
/cc @cockroachdb/release
TestSQLStatsPersistedLimitReached would previously flake because it did not consider background SQL activity happening in the cluster.
This commit re-writes the test to only make assertions that are not dependent on background cluster activity.
Resolves #105846, #97488
Epic: none
Release note: None
Release justification: Test de-flake