Less dumb solution: Getting a key custody safe [1] and mounting it to the exterior of your house so you can lock up the key while you're out running. Ideally it would be mounted somewhere discreet (perhaps inside a fake utility enclosure, which would also help protect it from the weather) but in plain view of the street so if someone does attempt to break in they're forced to draw attention to themselves.

You also have to be careful to get one that suits your threat model, a key custody safe designed to be installed in a semi-secure part of a building may not be resistant enough when mounted on the exterior with street access - many are only designed to resist covert tampering and are not that strong against a determined attacker with an angle grinder or similar overt attack.

[1] something like this: https://www.safeguardsafes.com.au/product/cmi-class-b-key-cu... - includes a very nice Kaba X-10 lock that is kinetically powered so you don't have to worry about wiring it to mains power or changing batteries.

I have a beehive in the garden, I just put the spare key in there.