I don't have a lot of experience with PG full text search in production or a bigger scale. I'd just suspected that it doesn't perform that well if you need a lot of filters, range queries etc? Maybe someone with more experience can chime in.
At work we just materialize the data from PG into ES and take advantage of the powerful ES queries and redundancy. Scaling up by just adding nodes is easier.
For our use case we don't really need a strict verification. Everything that should go to ES is put in a queue (using DB triggers) and then sent off to ES. If something should cause errors we'd see that by observing the error rate on ES ingest I assume.
Depends on the use case. We use it alongside Cassandra and MySQL, but we also deal with tens of billions of records. If you just have a webblog, you could just use elastic.
At work we just materialize the data from PG into ES and take advantage of the powerful ES queries and redundancy. Scaling up by just adding nodes is easier.