## Summary

Fix unnecessary Lit host updates in `@tanstack/lit-query` when refreshed controller state is referentially new but semantically unchanged.

This closes a render-loop/crash path with function-backed query options ( followup for [10716](https://github.com/TanStack/query/pull/10716) ) and restores default tracked-result behavior for query controllers.

## 🎯 Changes

- Suppress controller-triggered `requestUpdate()` calls during Lit’s active `hostUpdate` phase.
- Reuse observer current results instead of publishing fresh optimistic results on stable option refreshes.
- Track accessed query result fields for `createQueryController`, `createInfiniteQueryController`, and `createQueriesController`.
- Keep `createQueriesController` subscription handling on the emitted result to avoid per-emit option defaulting.
- Sync accessor reads from observer state so suppressed tracked notifications do not leave later reads stale.
- Apply structural sharing to `useMutationState` selected results.


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## ✅ Checklist

- [ ] I have followed the steps in the [Contributing guide](https://github.com/TanStack/query/blob/main/CONTRIBUTING.md).
- [x] I have tested this code locally with `pnpm run test:pr`.

## 🚀 Release Impact

- [x] This change affects published code, and I have generated a [changeset](https://github.com/changesets/changesets/blob/main/docs/adding-a-changeset.md).
- [ ] This change is docs/CI/dev-only (no release).


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## Summary by CodeRabbit

* **Bug Fixes**
  * Fixed unnecessary host updates that occurred when query results remained structurally unchanged, significantly improving application performance and reducing re-renders.
  * Optimized update handling for various query operations including refetching, infinite queries, and mutation state tracking.
  * Enhanced result stability when using selector functions and tracked result reads.

* **Tests**
  * Added comprehensive test coverage validating update behavior and result stability across query and mutation scenarios.

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