feat(workspace): split menus start AI tools; drop the Tools menu

A pane's split right/down menus offered only New terminal. They now list
the same AI tools as the tab bar's + menu (newTabTools/newTabBody,
shared from ConsoleTabs), started bare in the first free slot on that
side of the pane.

The tab bar's Tools menu is gone: its readme run hit 409 ERUNLIVE
whenever slot 0 was live (always, in the session view) and depended on
a personal skill; MCP sync and the dev-sync check served the dormant
ship-feature-lane pipeline. The sidebar row menu's readme item goes too.
The routes stay, reached by `agenthub lanes mcp sync` and
`agenthub lanes sync-base`.

Also: the home's Memory header and file tabs no longer shrink (a long
file squeezed the tab row and clipped it).

client/src/lib/api.ts

@@ -2917,16 +2917,6 @@ export const api = {
         `/lanes/${id}/profile/init`,
         { method: "POST", body: JSON.stringify({ force }) }
       ),
-    syncBaseCheck: (id: number, branch?: string) =>
-      request<{
-        code: number;
-        devDelta?: string[] | null;
-        overlap?: string[] | null;
-        collisions?: { file: string; collidesWith: string; suggestion: string }[];
-      }>(`/lanes/${id}/sync-base`, {
-        method: "POST",
-        body: JSON.stringify({ mode: "check", branch }),
-      }),
   },
   // ──────────────────────────────── Locks API ────────────────────────────────
   /** Named locks across all lanes: used for serialization and gating.