Update Claude owners (#6493)

Author: theMickster

.github/CODEOWNERS

@@ -102,3 +102,8 @@ util/RustSdk @bitwarden/team-sdk-sme
 # Multiple owners - DO NOT REMOVE (BRE)
 **/packages.lock.json
 Directory.Build.props
+
+# Claude related files
+.claude/ @bitwarden/team-ai-sme
+.github/workflows/respond.yml @bitwarden/team-ai-sme
+.github/workflows/review-code.yml @bitwarden/team-ai-sme