Move to an options variant for Show method in GlicInstanceImpl

This CL introduces `ShowOptions` as a variant to manage different Glic UI embedder types, such as the side panel and floating UI. This change improves type safety and decouples conversation switching logic from the specific UI embedder. `ShowOptions` also allows passing additional information for showing a UI that doesn't belong in the `EmbedderKey`.

Key changes:
- Introduced `glic::ShowOptions`, `glic::SidePanelShowOptions`, and
  `glic::FloatingShowOptions` to represent different ways to show the
  Glic UI.
- Removed the now-unnecessary `GlicInstanceImpl::EmbedderType` enum in
  favor of the `ShowOptions` variant.
- Updated `GlicInstanceImpl` and `GlicInstanceCoordinatorImpl` to use
  `ShowOptions`.
- `SwitchConversation` is now embedder-agnostic, simplifying the logic.

Fixed: b:450562729, b:450680703
Change-Id: I6a6a6964f47c81e352dd03461ff06d53153dc202
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/7032584
Commit-Queue: Trevor Perrier <perrier@chromium.org>
Reviewed-by: Trevor Perrier <perrier@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1528439}