How can I trigger this to run automatically—without tapping for confirmation?
You can't.
Normally, you could make an automation (or convert your shortcut into an automation), disable "Ask Before Running" and click "Don’t Ask to confirm your choice" (see this Apple Support article for more info and guidance).
I have a simple shortcut that turns on airplane mode when I arrive home.
Unfortunately, the aforementioned method mentioned above won't work for location-based automations (as well as other categories of automations). From Enable or disable a personal automation in Shortcuts on iPhone or iPad - Enable an automation to run without asking:
The following automations cannot be run automatically:
- Arrive
- Leave
- Before I Commute
- Message
- Wi-Fi
- Bluetooth
Emphasis mine
That was probably made like that for security purposes concerning possibly sensible informations.