Complete update check implementation - all tests passing

- Verified --no-check-update flag works correctly
- Confirmed CI mode detection works
- Tested update check runs non-blocking
- All linting and formatting checks pass

Co-authored-by: pelikhan <4175913+pelikhan@users.noreply.github.com>

Author: Copilot

pkg/cli/update_check_test.go

@@ -86,7 +86,7 @@ func TestShouldCheckForUpdate(t *testing.T) {
 			} else {
 				os.Setenv("CI", tt.ciEnv)
 			}
-			
+
 			if tt.mcpEnv == "" {
 				os.Unsetenv("GH_AW_MCP_SERVER")
 			} else {