Let's add automatically populated 'created_date' and 'modified_date' fields on relationships that act like the ones on activities. This could be useful to all CiviCRM users, not just WMF, so we can make the change in Civi core. Here's the upstream change proposal, with a comment in favor: https://lab.civicrm.org/dev/core/-/issues/2938
This ticket originally requested to make the start_date automatically set to the date of the relationship's creation in the database, but since start_date has a specific meaning it feels better to add these new columns.