It seems like some kind of network logging would be useful? Even if you don't catch it, you'd want to know what it did.
I've toyed with the idea of MITMing all connections and blocking any that I can't decrypt, but too much software has pinned certificates these days. (Too much for me, not in general)
Yeah agree.
In other comments I've mused about capturing data to be compared to the secret dataset, I'm sure it'd be possible to hash or something so that the proxy/sandbox doesn't have the data but can check it, or because it's not an agent it can call of to the data store for that.
Then you can just collect sequential blocks of data the agent sends out that match to sequences in the dataset. The longer the matching sequence the heavier it weights it. Single byte matches are almost always incidental, but individually sent bytes over time that line up with a n byte sequence in the source data is sus. And larger sequences of bytes send in one go that line up are immediately sus. If the weight ends up too high the agent is paused/walled off and an investigation called for.