I'd like to throw my vote in for this feature as well. I think it's entirely possible (and necessary) to develop a branch of personal data storage querying without doing anything silly regarding commodifying it.
After all, the two major things we often want to search are, in broad categories, the outside world and the inside world. Currently Kagi does the first one of those very well, but has very little (nothing) for the latter.
You can develop this with privacy centered at its core. It's your data, only you can access it. Just like your billing info or account details, but larger. Opt in if you want it, don't do anything if you don't. As a recent migrant from Google, I don't think I'm alone in this sentiment. Like OP, I've searched My Activity numerous times for a variety of reasons, and I'd be lying if I said I didn't miss it sorely.
If an "opted out by default" option isn't good enough for a certain privacy obsessed minority of your customer base, in the interest of preserving (and improving) the service for the rest of the customers I think it would be a wise business decision to start going at least a bit in this direction with Kagi.