It's open source. You can get as many details as you like :)

https://github.com/vitessio/vitess

https://vitess.io/docs/reference/vreplication/

https://vitess.io/docs/reference/features/vtgate-buffering/

Not sure how they do it, but I would do it like so:

Have old database be master. Let new be a slave. Load in latest db dump, may take as long as it wants.

Then start replication and catch up on the delay.

You would need, depending on the db type, a load balancer/failover manager. PgBouncer and PgPoolII come to mind, but MySQL has some as well. Let that connect to the master and slave, connect the application to the database through that layer.

Then trigger a failover. That should be it.