refactor(ui): full rewrite instance and code struct (#129)

## Summary by Sourcery

Refactor the UI to modernize effect handling, routing, and legacy APIs
while adding a reusable alert dialog component and cleaning up obsolete
stores.

New Features:
- Introduce a shared SaturnEffect context via ParticleBackground so
pages can access the effect without relying on global window APIs.
- Add a Base UI–powered alert dialog component for consistent
confirmation and warning flows across the app.
- Define a central router configuration module with instance routes to
standardize page wiring.

Bug Fixes:
- Ensure SaturnEffect nullish checks are handled safely when forwarding
pointer and touch events from the home view.

Enhancements:
- Rewrite ParticleBackground to manage its own SaturnEffect lifecycle
via React state and context instead of global accessors.
- Update the home view to use the SaturnEffect hook, simplify
pointer/touch handlers, and remove legacy game and release store usage.
- Refine layout and accessibility attributes for various form field and
label components, including field grouping and error rendering keys.
- Simplify sidebar navigation and adjust the user dropdown trigger to
work with the updated dropdown menu API.
- Wrap the root outlet for the home route with ParticleBackground only
on the index path to limit the effect to the intended view.
- Clean up imports and code style in radio group and other UI primitives
for consistency.

Chores:
- Remove deprecated UI stores and utility modules that are no longer
used with the new architecture.
- Add changeset entries documenting the Saturn effect refactor,
ParticleBackground rewrite, and removal of legacy store code.

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