Independent deployment is the property that makes a service a service, and a shared schema removes it regardless of how the code is organised.
the tests, all three of which must pass:
can it be deployed without deploying the other?
does it own its data, exclusively?
can it survive the other being down?
shared database → no to the first two. a column rename
is a coordinated release, which is the thing you were
trying to escape.
The usual path to this is splitting the code first and the data later, and later never arrives because it is the hard half. The result has the operational cost of two deployments, the network in the middle, and none of the independence — which is strictly worse than the monolith it replaced. A modular monolith with enforced boundaries gets most of the organisational benefit and can be split when the data is genuinely separated.