Recovery in Postgres is simplified and sped up considerably by the approach taken to MVCC. Same is true with transaction rollback. SQL Server users (on recent SQL Server versions) can optionally get a similar trade-off by enabling constant time recovery (CTR), which is called Accelerated Database recovery (ADR) in the MS marketing material. See the paper:

https://www.microsoft.com/en-us/research/uploads/prod/2019/0...

SQL Server has something called "background cleanup" when this feature is enabled, which takes place in a separate process called "the cleanup process" - just like VACUUM. The paper itself explicitly acknowledges the similarity. All of the advantages the paper claims for CTR/ADR are also advantages for Postgres.

It's also true that both traditional SQL Server (SS with ADR/CTR disabled) and MySQL have background cleanup processes of their own for indexes, but that is a little different. It's about asynchronously reclaiming space for index entries that were already delete-marked.