This is uninteresting. It is fully expected that foreign countries know about (and extensively surveil) your "official cover" embassy staff intelligence officer

This is uninteresting. It is fully expected that foreign countries know about (and extensively surveil) your "official cover" embassy staff intelligence officers. We tailed everyone who stepped out of the Soviet embassy for most of the Cold War. Those people are administrators. Your actual covert operatives will never interact with the embassy in a detectable/obvious way.