I've tried adding the_wait_begin/thd_wait_end into MYSQL_BIN_LOG::wait_for_update_bin_log where the thread waits for a conditional variable. This had an immediate effect on the reaction time. (Attached patch yield_wait_for_update_bin_log.diff)

I couldn't compile the Debian package without commenting out the tests (and I actually had to backport two patches to even compile in the first place), but all the failed tests seems to be related the SSL, and at least one of the failures was caused by an expired certificate.

Anyway, the patch is currently running in the internal databases at my work place, to see if it have any unwanted side-effects.

The SSL certificates issues are due to the fact the the certs used for the test suite have expired, it has been solved since on MDEV-7536 so you can disregard those tests.
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About your issue, i had issues on a slave running pool-of-threads that could be related : MDEV-5951.
That slave was having dumps for each databases running sequentially while at the same time there was another thread dumping the databases structures (also sequentially) and one the table contents and i was hitting the "thread_pool_max_threads" limit (which was not low) on one of the dumps at some point while the only connections to the server were the dumps and a simple moitoring Zabbix script that was just checking some server variables every minutes.
Disabling the threadpool made the issue to go away.

Do you think this bug could produce that kind if issue?

I doubt that it is related to MDEV-5951, which looks like somebody forgetting to unlock LOCK_thread_count somewhere.

Thanks for the report and the patch. Below is a simple MTR test case to confirm the problem (not to be included to the regression suite).

Results with and without the patch on the current 5.5 tree, debug build:

# Min connection time:   1366
# Max connection time:   997304 
# Total connection time: 16919926
# Avg connection time:   338398.5200

# Min connection time:   1370
# Max connection time:   1965 
# Total connection time: 78925
# Avg connection time:   1578.5000

# Min connection time:   1274
# Max connection time:   2034 
# Total connection time: 74009
# Avg connection time:   1480.1800

# Min connection time:   1419
# Max connection time:   2322 
# Total connection time: 85742
# Avg connection time:   1714.8400

So the patch does help, although I don't know if it's otherwise correct.

--source include/master-slave.inc
--source include/have_binlog_format_statement.inc

--let $num = 50
--let $sum = 0
--let $max = 0
--let $min = 10000000
--let $n = $num
while ($n) 
{
	--let $before = `select now(6)`
	--connect (con$n,localhost,root,,)
	--let $tm = `select timestampdiff(microsecond,'$before', now(6))`
	--echo # Connection time: $tm
	--let $sum = `select $sum + $tm`
	--let $max = `select if($tm>$max,$tm,$max)`
	--let $min = `select if($tm<$min,$tm,$min)`
	--connection default
	--dec $n
}

--let $avg = `select $sum / $num`

--echo # Min connection time:   $min
--echo # Max connection time:   $max 
--echo # Total connection time: $sum
--echo # Avg connection time:   $avg

--source include/rpl_end.inc

We have the same problem on servers with thread pool.