`+choices` sync `localStorage` with Bati 🔗

When the user clicks on `Vue` at https://vike.dev/new it should automatically select `vue` in +choices.

Supersedes:
- https://github.com/brillout/docpress/issues/92

Start by reproducing the behavior at https://vike.dev/new: click Vue and inspect how the selection is stored in localStorage and consumed by +choices. Trace the +choices integration and Bati interaction from there. Done means clicking Vue automatically selects vue in +choices and the selection remains synchronized.

Written by the indexing model from the issue text.