Spring's default lets HttpRequestMethodNotSupportedException escape to the
catch-all @ExceptionHandler(Exception.class), surfacing as a 500 with a full
stack trace. Return a clean 405 so the client gets a structured R body and
the log stays at WARN.
This is also the second line of defence against malformed path segments that
confuse reverse proxies — e.g. a conversationId ending in ":" can make a
proxy strip the trailing path, landing a GET /api/v1/conversations/<id> on
the @DeleteMapping variant and triggering exactly this exception (issue #369).
