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/constants.ts

@@ -27,6 +27,7 @@ export const CHECK_IDS = {
   DEP_AST_GREP_CLI: "dep-ast-grep-cli",
   DEP_AST_GREP_NAPI: "dep-ast-grep-napi",
   DEP_COMMENT_CHECKER: "dep-comment-checker",
+  GH_CLI: "gh-cli",
   LSP_SERVERS: "lsp-servers",
   MCP_BUILTIN: "mcp-builtin",
   MCP_USER: "mcp-user",
@@ -43,6 +44,7 @@ export const CHECK_NAMES: Record<string, string> = {
   [CHECK_IDS.DEP_AST_GREP_CLI]: "AST-Grep CLI",
   [CHECK_IDS.DEP_AST_GREP_NAPI]: "AST-Grep NAPI",
   [CHECK_IDS.DEP_COMMENT_CHECKER]: "Comment Checker",
+  [CHECK_IDS.GH_CLI]: "GitHub CLI",
   [CHECK_IDS.LSP_SERVERS]: "LSP Servers",
   [CHECK_IDS.MCP_BUILTIN]: "Built-in MCP Servers",
   [CHECK_IDS.MCP_USER]: "User MCP Configuration",