#28127 carry of #27649: Home tab animation routing

Carry of #27649: cmux NEXT: a tab Home opens to the right opens only where it lands.

Original purpose: keep Home-dock tabs out of the Home strip while they move beside the dock, so the open animation plays only where the tab lands. This carry preserves the original commits, resolves the current base conflict, and merges feat-cmux-next.

Original PR: https://github.com/manaflow-ai/cmux/pull/27649
Before/after capture from the original PR: before / after
No capture: the original before/after captures linked above show this unchanged Home-dock behavior. This carry only merges base and restores the outbound declaration; it adds no new visual state.

Agent session: agent session