web+coder: segmented per-agent slash menu (agent commands + skills) + cross-agent skill execution

Coder / menu now shows two groups: the active agent's commands first (manifest + live ACP available_commands), BooCoder skills second. SlashCommandPicker gains an opt-in groups prop (flat items path unchanged -> BooChat byte-identical, parity verified); ChatInput takes slashGroups; CoderPane builds the groups. Skills run under the selected agent: coder skill_invoke accepts a provider and, when external, injects the server-side skill body into a dispatched task instead of native inference. Also folds in the initial-chat skill fix (handleLandingSkill: create chat -> assign to pane -> invoke, same transition as a text send) that resolves the landing-page blank screen. BooChat slash menu + skill invocation unchanged.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

apps/web/src/components/Workspace.tsx

@@ -82,6 +82,7 @@ export function Workspace({
     deleteChat,
     renameChat,
     handleLandingSend,
+    handleLandingSkill,
   } = chatsHook;
 
   const { isMobile } = useViewport();
@@ -387,6 +388,7 @@ export function Workspace({
                   onAgentChange={onAgentChange}
                   createChat={() => api.chats.create(sessionId)}
                   onSend={(content) => void handleLandingSend(idx, content)}
+                  onSkillInvoke={(skillName, userMessage) => void handleLandingSkill(idx, skillName, userMessage)}
                 />
               )}
             </div>