If you're not sure if those logs are related, perhaps you should run "date" when things get slow and find the relevant debug logs that way?
I didn't see any smoking gun in what you posted, but since you're posting about "slow" with a log describing filter processing I'd look into unindexed searches. You're using syncrepl, so hopefully you read in the slapo-syncprov man page
On databases that support inequality indexing, it is helpful to set an eq index on the entryCSN attribute when using this overlay.
and followed that advice? If you added indices, did you run slapindex after stopping slapd? Look for messages along the lines of
<= bdb_equality_candidates: (FOO) not indexed
in your logs.