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/components/lanes/WorkspaceHome.tsx

@@ -894,7 +894,7 @@ function HomeBody({
             onKeyDown={(e) => e.key === "Escape" && setMemoryOpen(false)}
             className="flex max-h-[85vh] w-full max-w-3xl flex-col rounded-xl border border-border bg-surface-1 p-5 shadow-xl"
           >
-            <div className="mb-3 flex items-center justify-between">
+            <div className="mb-3 flex shrink-0 items-center justify-between">
               <h2 className="text-sm font-semibold text-fg-primary">{t("home.memory")}</h2>
               <button
                 type="button"
@@ -909,7 +909,10 @@ function HomeBody({
             <div
               role="tablist"
               aria-label={t("home.memory")}
-              className="mb-3 flex gap-1.5 overflow-x-auto border-b border-border/60 pb-2 no-scrollbar"
+              // shrink-0: a horizontal scroller's min-height is 0, so in this
+              // height-capped column a long file squeezed the row and clipped
+              // the tabs. The panel below is the one part that scrolls.
+              className="mb-3 flex shrink-0 gap-1.5 overflow-x-auto border-b border-border/60 pb-2 no-scrollbar"
             >
               {memory.map((f, i) => (
                 <button