feat(tabs,app): tab id handles, fixed-width tabs-lift, slim shell + full-height sidebar

Tabs:
- short-handle ID badge per tab (shortest unique conversationId prefix, min 4)
- fixed-width (w-48) tabs with tabs-lift folder borders

Shell (composition root):
- drop the Dispatch title bar; tabs sit at the very top with a 5px gap
- big faded "Dispatch" watermark centered on an empty chat
- collapsible right sidebar (empty shell) spanning full window height: a
  permanently right-pinned hamburger in the tab row toggles it; in-flow push
  that shrinks the whole left column (tabs included) at >=lg, overlay + backdrop
  below lg; open-by-default on wide / closed on narrow
- main is overflow-hidden with a min-w-0 shrink chain; app.css pins
  html/body/#app height + body overflow hidden so the page never overflows

1 files changed, 19 insertions, 0 deletions

diff --git a/src/features/tabs/tabs.ts b/src/features/tabs/tabs.ts
index a4db6f3..61ae58e 100644
--- a/src/features/tabs/tabs.ts
+++ b/src/features/tabs/tabs.ts
@@ -92,3 +92,22 @@ export function deriveTitle(message: string, max: number = DEFAULT_MAX_TITLE_LEN
 	if (trimmed.length <= max) return trimmed;
 	return `${trimmed.slice(0, max)}\u2026`;
 }
+
+/** Minimum length of a tab handle (git-style short id). */
+export const MIN_HANDLE_LENGTH = 4;
+
+/**
+ * The short "handle" shown on a tab: the shortest prefix of `conversationId`
+ * (at least `MIN_HANDLE_LENGTH` chars) that is unique among all open tabs — a
+ * git-style short id. Grows by a char only when another open tab shares the
+ * prefix, and shrinks back when that sibling closes. Pure: the id + every open
+ * id in, the handle string out. (`allIds` may include `conversationId` itself.)
+ */
+export function shortHandle(conversationId: string, allIds: readonly string[]): string {
+	const others = allIds.filter((id) => id !== conversationId);
+	for (let len = MIN_HANDLE_LENGTH; len < conversationId.length; len++) {
+		const candidate = conversationId.slice(0, len);
+		if (!others.some((id) => id.startsWith(candidate))) return candidate;
+	}
+	return conversationId;
+}