Verify impact of increased statistic collection to HAF performance stability

We observed lately (probably because of upgrade to Psql14) systematic performance degradation of HAF instances in time. Running there vaccumm analyze usually solved the problem (although it should be done automatically).

We should try and verify on syntectic benchmarks like also by prod traffic redicection (and collecting timing info) following changes described in this thread: HAfAH!69 (comment 123859)