feat(mobile): synchronized pill composer transitions and draft screen fixes

Drop the animated pill/composer morph in favor of instant swaps that are
synchronized with the keyboard choreography: a new oc:keyboard-intent
event collapses the composer (flushSync) before the hide compensation is
measured, so keyboard travel and composer height change land as a single
chat motion on both iOS and Android (Android also gains keyboard signals
and deterministic re-pins around its native resize). The WKWebView caret
is hidden during the transition so it no longer flies to its new position.

Draft screen: starter chips hide instantly while the keyboard is up and
the centered title rides the keyboard shift compensation instead of
double-jumping; the composer drag handle also works in dictation mode;
the highlight mirror is disabled on mobile so the caret matches the text.

Fixes: worktree discovery and the GitHub auth probe now wait for the
runtime connection (no more empty branch pickers / stale auth on cold
start), worktree discovery merges per project instead of clobbering the
persisted map, the cross-project session list resets on instance switch
(with an in-flight load guard) so no stale sessions linger, and mobile
overlay content contains its overscroll instead of bouncing the page.

packages/ui/src/components/chat/ChatContainer.tsx

@@ -801,7 +801,7 @@ export const ChatContainer: React.FC<ChatContainerProps> = ({ autoOpenDraft = tr
 		return (
 			<div className="relative flex h-full flex-col bg-background transform-gpu">
 				{useCompactDraftLayout && !isDesktopExpandedInput ? (
-					<div className="flex min-h-0 flex-1 flex-col items-center justify-center px-6 text-center">
+					<div className="oc-draft-center flex min-h-0 flex-1 flex-col items-center justify-center px-6 text-center">
 						<h1 className="text-balance text-3xl font-normal tracking-tight text-foreground">
 							{renderDraftTitle(
 								draftProjectLabel
@@ -812,7 +812,7 @@ export const ChatContainer: React.FC<ChatContainerProps> = ({ autoOpenDraft = tr
 						</h1>
 						<DraftPresetChips
 							onSubmit={(text) => useInputStore.getState().requestPresetSubmit(text)}
-							className="mt-8 max-w-md"
+							className="oc-draft-starters mt-8 max-w-md"
 						/>
 					</div>
 				) : null}