Feat lit-query: add initial lit-query package

[chughgaurav]

🎯 Changes

Adds an initial @tanstack/lit-query package that brings TanStack Query Core to Lit via reactive controllers.

• New Features

Included in this PR:

• QueryClientProvider and query-client resolution helpers
• query, mutation, infinite-query, and queries controllers
• useIsFetching, useIsMutating, and useMutationState
• queryOptions, infiniteQueryOptions, and mutationOptions
• Lit examples covering basic usage, pagination, and SSR
• unit/type tests for controller lifecycle, client switching, counters/state, and inference

• Documentation

  • New package README with installation, quick-start, API surface, and example instructions.

• Tests / E2E

  • Comprehensive unit + Playwright E2E suites and helpers covering smoke, error recovery, lifecycle, pagination, mutations, and SSR.

Notes

This PR is focused on the initial package integration and API surface for Lit.

✅ Checklist

• I have followed the steps in the Contributing guide.
• I have tested this code locally with pnpm run test:pr.

🚀 Release Impact

• This change affects published code, and I have generated a changeset.
• This change is docs/CI/dev-only (no release).

Summary by CodeRabbit

• New Features
  • Added @tanstack/lit-query package, a TanStack Query integration for Lit components
  • Introduced reactive controllers for queries, mutations, and infinite queries
  • Added QueryClientProvider component for context management
  • Included hooks for tracking fetching/mutating state and mutation status
  • Provided example applications demonstrating pagination, server-side rendering, and core functionality