I went through a similar switch from MSSQL to postgres. We moved 7 applications of various sizes over and the biggest hurdle was office politics. The migration never took more than a day for each app. ETL and reporting were not affected since we had previously integrated messaging (rabbitmq) pretty heavily into every system at the company and ETL gets their data from there.

We also switched the DB servers to over to linux and got a huge performance boost from that.

We did rewrite some stuff, but that was mostly to take advantage of postgres features like array types (instead of a article tags table, you'd have an tags array) which we used to speed up some applications. One we sped up by a factor of 10, just by using array types and offloading json generation to postgres: select array_to_json(array_agg(row_to_json(t))) from ( some query ) t

It was several smaller apps written with most logic in the app (Hibernate) and had very little T-SQL/stored procs. We also weren't using any of the add-ons like SQL reporting, etc. The big commercial DBs have the advantages when you start using their reporting services, BI/OLAP stuff...and likely when you have several different groups as stakeholders in the process...