Trellis doesn’t handle database updates by default.
What you’re describing sounds like database migrations and seeding, something that is not included with WordPress, and not something I’ve ever actually seen happen with it. But holy crap could WP use it, however it’s a very developer centric feature so nothing that will ever be added into WP core.
Many people once they get into a multiple developer project, have only a couple options that I’ve seen used successfully. I think that generally, developers need to be in communication about who’s doing what with the database.
There were some interesting suggestions here: Syncing WordPress Database Changes Between Environments: How We Handle Merging in 2022
This can help with keeping site settings in version control: https://github.com/danielbachhuber/dictator
This is an expensive plugin but really the only one I’ve seen that is able to do a true database comparison and merge: https://crowdfavorite.com/ramp/
This has also been discussed quite a few times previously:
https://discourse.roots.io/t/keep-database-synced-between-computers-in-trellis-bedrock-sage-setup/4478
https://discourse.roots.io/t/syncing-databases-between-mulitple-developers-and-server/4078
https://discourse.roots.io/t/best-practices-for-syncing-the-development-database-between-multiple-developers-machines-with-bedrock-ansible/3954