chore: Update with-svelte example (#13118)
## Summary
- update the example to Svelte 5.56.9, SvelteKit 2.70.2, TypeScript
7.0.2, ESLint 10.8.1, Vite 8.2.1, Vitest 4.1.10, Turbo 2.10.10, and pnpm
11.22.0
- expose the internal UI package from source and sync SvelteKit before
TypeScript checks
- enable the shared Turbo ESLint flat config and consolidate Svelte
dependencies in a pnpm catalog
- retain the unit and browser component coverage, centralized ignore and
formatting configuration, and explicit Turbo task relationships
- add the missing Playwright dependency, refresh Svelte documentation
links, and remove obsolete package-build configuration
- sync the branch with the latest `main`
## Validation
- `pnpm install --frozen-lockfile`
- `pnpm exec turbo run build check-types lint test:unit
--continue=always`
- `pnpm format:check`
- repository pre-push hooks
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Co-authored-by: Anthony Shew <anthonyshew@gmail.com>
