feat(doctor): add GitHub CLI check (#384)

Add doctor check for GitHub CLI (gh) that verifies:
- Binary installation status
- Authentication status with GitHub
- Account details and token scopes when authenticated

Closes #374

Co-authored-by: sisyphus-dev-ai <sisyphus-dev-ai@users.noreply.github.com>

src/cli/doctor/checks/index.ts

@@ -4,6 +4,7 @@ import { getPluginCheckDefinition } from "./plugin"
 import { getConfigCheckDefinition } from "./config"
 import { getAuthCheckDefinitions } from "./auth"
 import { getDependencyCheckDefinitions } from "./dependencies"
+import { getGhCliCheckDefinition } from "./gh"
 import { getLspCheckDefinition } from "./lsp"
 import { getMcpCheckDefinitions } from "./mcp"
 import { getVersionCheckDefinition } from "./version"
@@ -13,6 +14,7 @@ export * from "./plugin"
 export * from "./config"
 export * from "./auth"
 export * from "./dependencies"
+export * from "./gh"
 export * from "./lsp"
 export * from "./mcp"
 export * from "./version"
@@ -24,6 +26,7 @@ export function getAllCheckDefinitions(): CheckDefinition[] {
     getConfigCheckDefinition(),
     ...getAuthCheckDefinitions(),
     ...getDependencyCheckDefinitions(),
+    getGhCliCheckDefinition(),
     getLspCheckDefinition(),
     ...getMcpCheckDefinitions(),
     getVersionCheckDefinition(),