fix(welcome): gate Claude and Opencode buttons on CLI availability too

Extends the Gemini gating from bb7fb9e to the other welcome-screen
buttons that had the same problem: shown unconditionally even when the
underlying CLI isn't installed.

- Add isClaudeAvailable() (claude-cli-resolver.ts) and GET
  /api/claude/status, mirroring the existing opencode/codex/gemini
  resolvers and status endpoints.
- Opencode already had a working /api/opencode/status the welcome
  screen just wasn't checking; wire it up the same way.
- Refactor loadGeminiAvailability() into a shared
  _loadCliAvailability(buttonId, statusUrl) helper instead of
  duplicating the fetch/try-catch three times.

Run-mode dropdown entries (Opencode/Codex) are intentionally left
unconditional here — follow-up PR.

src/web/public/index.html

@@ -311,11 +311,11 @@
           <h1 class="welcome-title">Codeman</h1>
           <p class="welcome-desc">Manage AI Coding tools in persistent tmux sessions.</p>
           <div class="welcome-actions">
-            <button class="welcome-btn welcome-btn-claude" onclick="app.setRunMode('claude'); app.runClaude()">
+            <button class="welcome-btn welcome-btn-claude" id="welcomeClaudeBtn" style="display: none;" onclick="app.setRunMode('claude'); app.runClaude()">
               <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><polygon points="5 3 19 12 5 21 5 3"/></svg>
               Run Claude Code
             </button>
-            <button class="welcome-btn welcome-btn-opencode" onclick="app.setRunMode('opencode'); app.runOpenCode()">
+            <button class="welcome-btn welcome-btn-opencode" id="welcomeOpencodeBtn" style="display: none;" onclick="app.setRunMode('opencode'); app.runOpenCode()">
               <svg width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><polygon points="5 3 19 12 5 21 5 3"/></svg>
               Run OpenCode
             </button>