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/utils/claude-cli-resolver.ts

@@ -26,6 +26,15 @@ const CLAUDE_SEARCH_DIRS = [
 /** Cached directory containing the claude binary (empty string = searched but not found) */
 let _claudeDir: string | null = null;
 
+/**
+ * Returns true if the Claude CLI binary can be located (via `which` or one of
+ * the common install directories). Mirrors `isGeminiAvailable`/`isOpenCodeAvailable`/
+ * `isCodexAvailable` in the sibling resolvers.
+ */
+export function isClaudeAvailable(): boolean {
+  return findClaudeDir() !== null;
+}
+
 /**
  * Finds the directory containing the `claude` binary.
  * Checks `which claude` first, then falls back to common install locations.