fix(carousel): improve carousel context handling with async context

[IMinchev64]

Closes this Bug

Current carousel context wiring:

• The carousel sets up a Lit ContextProvider (carouselContext) when it constructs. Slides use @consume({ context: carouselContext, subscribe: true }) to grab a _carousel ref.
• The consumer request fires once when the slide connects. If the carousel isn't upgraded/publishing yet (common if Blazor renders wrappers and upgrades happen later), that request is missed and _carousel stays undefined.

Why this causes issues (Blazor timing):

• If I understand correctly, Blazor renders web components, then the custom elements upgrade. Slides can connect before the carousel has attached its provider. Because the consume decorator issues a one-time request, there's no retry, so the ref never gets set. Downstream slide logic that expects _carousel blows up.

Why refactor following tile manager:

• Tile manager uses an async context consumer created after updateComplete, and the provider re-sets its value once ready. This avoids the race.
• Copying that pattern (or otherwise deferring/retrying the context request) ensures slides always get a valid carousel ref, eliminating the timing gap seen in Blazor.

[Copilot]

Pull request overview

This PR addresses a race condition in carousel context initialization that occurs when slides connect before the carousel component has fully upgraded, particularly in Blazor scenarios. The fix replaces the synchronous @consume decorator with an async context consumer pattern (borrowed from tile-manager), ensuring slides reliably obtain their carousel reference regardless of initialization timing.

Key changes:

• Introduced async context consumer in carousel slides to handle delayed context availability
• Added explicit context setting in carousel's firstUpdated lifecycle hook
• Replaced all direct _carousel references with _carouselInstance getter for fallback logic

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 2 comments.

File	Description
src/components/carousel/carousel.ts	Extracts context setting into _setCarouselContext() method and calls it in firstUpdated() to ensure context is available after component upgrade
src/components/carousel/carousel-slide.ts	Replaces @consume decorator with async context consumer and adds _carouselInstance getter to provide fallback access pattern

[Copilot]

Pull request overview

Copilot reviewed 2 out of 2 changed files in this pull request and generated no new comments.