[Remote rendering 3.4] UI panel and theme state authority

### 📝 Description of the feature

Design question: do we want to sync the UI state to the server, so it can stay up to date, or do we want this to remain client-owned entirely?

Today, at save_state time, the UI state, like the rest of the state, is retrieved by the server through a client round trip. Do we want to continue this pattern for the UI state, which is independent of the VTK pipeline? Or do we want to use a sync-back pattern like the camera, and store the UI state metadata on the server, so that save_state doesn't require a client round trip, and so that a refresh or reconnect will preserve the UI state as well as the VTK pipeline?

If we want to keep the UI state purely client-side, there is no work here.

If we want it to be synced back to the server, then the TheiaUIState (panel collapsed/expanded, active tab index, dark/light theme) flows through the same save/load paths as camera and per-part state.

More details to be added in backlog grooming.

### Acceptance Criteria

- No in-visualizer behavior changes.
- Refresh behavior depends on the decision that gates the rest of this user story.

### 💵 Business Value

_No response_

### 🔗 Useful links and references

_No response_