Upgrade to PostgreSQL 17 mandatory for external db?

We are using Zammad with an external managed database at Digital Ocean. They currently are at PostgreSQL 16.

With the release of Zammad 6.4.0 there was this warning:

This includes a major update for the postgres dependency from 15 to 17, which requires manual action to upgrade the postgresql cluster data to the new version. Please see the postgres upgrading instructions for details.

The update from 6.3.1 to 6.4.0 went smoothly.
Do we have to expect any issues if we are at PostgreSQL 16?

You can find the minimum requirements for PostgreSQL (which thus affect your external database server) in the documentation. You should always ensure to stay above that limit:
https://docs.zammad.org/en/latest/prerequisites/software.html#database-server