RDS Proxy causes intermittent "Connection timed out" errors

Good day.

I have a problem after adding RDS Proxy to our service, "SQLSTATE[HY000] [2002] Connection timed out" started to appear. Though they are pretty infrequent (maybe 1/100,000 of connections or even less fail), the problem quickly became pretty annoying. Sometimes there is one or two per hour, sometimes none. Looks like the amount of errors correlates a little with the amount of connections made (it is hard to tell though).

Some info about the service:

• Aurora MySQL 3.03.1, 3AZ, 1 writer + 2 readers.
• PHP 8.1 + PDO extension (maybe that is a known issue that the advanced driver for Java solves?), connection attempt is stopped after about 30 seconds.

MySQL non-default parameters:

• sql_mode = TRADITIONAL
• max_connections = 500 (was useful before the proxy was introduced)
• long_query_time = 30
• binlog_format = MIXED (for blue-green deployments only)

RDS Metrics:

• AbortedClients: there are some, tens of such failures per day, but significantly more than 2-5 errors I see.
• ActiveTransactions: 0
• AuroraSlowConnectionHandleCount: 1.5k+ is added per day
• AuroraSlowHandshakeCount: 2-3 is added per day

RDS Proxy metrics are all green (no errors, connection pins, etc.). I've tried to enable advanced logging, there was not much to gain. Could see only that some connections were pinned due to the query size, but it was relatively rare, some per minute.

Thanks for any help.

If there are any folks that stumbled upon the same issue, feel free to complain here.