fix(doctor): detect gh when Bun.which misses it

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/cli/doctor/checks/tools-gh.test.ts

@@ -0,0 +1,35 @@
+/// <reference types="bun-types" />
+
+import { afterEach, describe, expect, it, mock } from "bun:test"
+
+const originalWhich = Bun.which
+
+afterEach(() => {
+  Bun.which = originalWhich
+  mock.restore()
+})
+
+describe("getGhCliInfo", () => {
+  it("falls back to gh --version when Bun.which cannot find gh", async () => {
+    // given
+    Bun.which = mock(() => null)
+    mock.module("../spawn-with-timeout", () => ({
+      spawnWithTimeout: mock((command: string[]) => {
+        if (command.join(" ") === "gh --version") {
+          return Promise.resolve({ stdout: "gh version 2.82.1\n", stderr: "", exitCode: 0, timedOut: false })
+        }
+
+        return Promise.resolve({ stdout: "", stderr: "not logged in", exitCode: 1, timedOut: false })
+      }),
+    }))
+    const { getGhCliInfo } = await import("./tools-gh")
+
+    // when
+    const info = await getGhCliInfo()
+
+    // then
+    expect(info.installed).toBe(true)
+    expect(info.version).toBe("2.82.1")
+    expect(info.path).toBe(null)
+  })
+})

src/cli/doctor/checks/tools-gh.ts

@@ -80,6 +80,20 @@ async function getGhAuthStatus(): Promise<{
 export async function getGhCliInfo(): Promise<GhCliInfo> {
   const binaryStatus = await checkBinaryExists("gh")
   if (!binaryStatus.exists) {
+    const version = await getGhVersion()
+    if (version) {
+      const authStatus = await getGhAuthStatus()
+      return {
+        installed: true,
+        version,
+        path: null,
+        authenticated: authStatus.authenticated,
+        username: authStatus.username,
+        scopes: authStatus.scopes,
+        error: authStatus.error,
+      }
+    }
+
     return {
       installed: false,
       version: null,