chore: update dependencies and adopt React/Vue eslint presets

[thetutlage]

Summary

• Bumps deps across all five kits to latest stable: @adonisjs/core 7.3.3, @adonisjs/eslint-config 3.1, eslint 10.4, typescript 6.0.3, @vinejs/vine 4.4, better-sqlite3 12.10, prettier 3.8.3, @types/node 25.9, plus framework-specific ones (@inertiajs/{react,vue3} 2.3.24, @vitejs/plugin-vue 6.0.7, vue 3.5.35, vue-tsc 3.3.2, react/react-dom 19.2.6, alpinejs 3.15.12, edge.js 6.5.1, turbo 2.9.16).
• Held back from majors that aren't ready: vite stays on 7 (@adonisjs/vite@5.1.1 doesn't accept vite 8 yet — only a 6.0.0-next.1 exists), @vitejs/plugin-react stays on 5 (v6 needs vite 8), @inertiajs/{react,vue3} stay on 2.3 (per maintainer preference).
• Wires the new React and Vue presets from adonisjs/eslint-config#15 into the inertia kits via configApp(...react) / configApp(...vue) and adds the required eslint plugins (eslint-plugin-react, eslint-plugin-react-hooks, eslint-plugin-vue).
• inertia-vue turns off vue/component-api-style for inertia/**/*.ts only — the rule false-positives on the render: key inside createApp({ render: () => h(...) }) in inertia/app.ts. SFCs still get it enforced.
• inertia-react adds npm overrides + pnpm.overrides to relax eslint-plugin-react@7.37.5's eslint peer range (still pinned to ≤9, blocks ERESOLVE on install with eslint 10). Can be removed once the plugin ships an eslint-10-compatible release.
• Drops the deprecated baseUrl: "." from inertia/tsconfig.json in both inertia kits (TS6 deprecation).
• Applies eslint --fix cleanups surfaced by the new presets: type-only imports, rel="noreferrer" on target=_blank links, v-slot longhand, attribute ordering, and a couple of small refactors (shadowed page rename in ssr.tsx, hoisting usePage().url out of a useEffect deps array).

Test plan

• npm install clean in all five kits (api, api-monorepo, hypermedia, inertia-react, inertia-vue)
• npm run lint passes
• npm run typecheck passes
• npm run build produces a build
• node bin/server.js from each kit's build directory returns HTTP 200 on /
• api-monorepo: turbo lint, turbo typecheck, turbo build all green