feat(appkit): offer the database plugin in databricks apps init

[ditadi]

Stacked on #674.

Summary

Offers the DatabasePlugin in databricks apps init, and documents the development flow end to end. The flow:

• appkit db init points .env at a Lakebase branch of your own.
• appkit db migrate writes and applies migrations as you change config/database/schema.ts.
• The deployed app applies the committed migrations on start.
• appkit db verify checks your branch, and with --prod the deployed app.
• One owner per branch: the app's service principal owns the schema on the deploy branch.

Details

• The plugin manifest is no longer hidden. The plugin barrel exports database, so beta.ts drops its explicit export. The appkit db commands are no longer hidden in the CLI.
• Template changes:
  • config/database/schema.ts uses schema app.
  • appkit.plugins.json gets the database entry, with the postgres binding for branch and database.
  • README.md.tmpl gets a development-workflow section and config/database/ in the project structure.
  • _gitignore skips config/database/*.bak, the previous schema.ts that introspect keeps.
• drizzle-kit is a template devDependency, since appkit db init/migrate generate migrations with it. check-template-deps keeps it at the version AppKit pins, and its skew message gives each synced dependency its reason.
  • Every scaffolded app gets it, with or without the plugin. apps init installs from the template's single committed lockfile (npm ci / pnpm --frozen-lockfile), so the dependency can't be dropped per app.
  • It is dev-only. Installs show two deprecation notices from drizzle-kit's own @esbuild-kit dependencies.
• The template locks gain drizzle-kit and its 59 dependencies, all from registry.npmjs.org. No existing package changes version.
• databricks apps init running appkit db init for you is a separate Databricks CLI change. This PR should land once a CLI release with that change is out.

Tests

• I checked the plugin docs and README claims against the code of feat(appkit): apply committed database migrations on deploy start #654–feat(appkit): add appkit db verify #674: init flags and branch choice, migrate/clean/seed refusals, the introspect migration name, and verify/--prod.
• I rendered README.md.tmpl with Go text/template and missingkey=zero, the way apps init does, for four plugin sets: none, analytics, database, and both.
• tools/check-template-deps.ts passes. With the template's drizzle-kit version changed, it reports the new skew message.
• Full gate passes: build, typecheck, lint/format, knip, generate:types and sync:template (no diff), the docs build, and 6075 tests.