Woodworker/developer Jesse Schutt clearly explains how to use v-model properly on nested components.

Building a custom component that operates on chunks of data is easier than you may think. It involves understanding how Vue handles the input/update cycle and making a few changes to your component. Let’s start by taking a look at one approach for turning a standard component into a “controlled” component and then figure out how to nest them.

https://zaengle.com/blog/using-v-model-on-nested-vue-components