If schema migrations take non-zero time and you want zero-downtime deployments, then the both service versions need to be compatible with either the new schema or the old schema, regardless of service size.
The software should be compatible with both the old and new schema until all of your database servers have moved over to the new schema. All rollouts are going to be somewhat staggered even if you go straight to 100%.
The same problem exists in microservoce land, only you now have a load of separate teams managing their own database, perhaps with different solutions.
Wait, micro-service and sharing same DB? Did I miss something?
I think you misunderstood what I said, which is you still have databases and ergo need to manage migrations and such, only that this now typically falls to the specific teams.
That said, loads of folks do microservices with a shared dB.