Postgres connector push down decision logic?

[StephenOTT]

Looking at https://trino.io/docs/current/connector/postgresql.html#pushdown

Trying to understand what logic is to use decide if push down should be done?

What table stats are used to make these decisions?

There is a list of aggregations that are supported, but what about all of the other functions in trino. Is there a listing of what functions would cause the push down to not happen? Example: date functions, casts, sub queries, IF statement, etc etc.

Additionally: https://trino.io/docs/current/connector/postgresql.html#cost-based-join-pushdown

States: "Note that if no table statistics are available, join operation pushdown does not occur to avoid a potential decrease in query performance."

Can you explain or provide a ref to the underlying logic for this statement? In which scenario would NOT using the underlying jdbc db source to do the join be preferred? / in which scenario is it better to do the joins, etc in trino instead of pushing down into the Db through a jdbc connection?

Thanks.