Usage of java.time.Clock for timestamps isn't consistently performed in Pulsar code base

In some of the existing code locations, PulsarService's `java.time.Clock clock` field is used for timestamps, however it's not consistently applied in the code base. Would it be useful to use `java.time.Clock` for timestamps?

_Originally posted by @lhotari in https://github.com/apache/pulsar/pull/25658#discussion_r3178499222_

Start by locating PulsarService's java.time.Clock field and inventorying the other timestamp-producing code locations in the Pulsar code base. Determine which locations bypass the clock, then define completion as consistent clock usage across the identified cases with appropriate validation; the issue names no files or tests.

Written by the indexing model from the issue text.