Can't get past the iPhone "Trust this computer" loop

iPhone with ios 16.6.1 and Macbook Air with OS 10.14.6

I've read older, closed topics on here about this problem. The instructions in About the 'Trust This Computer' alert message on your iPhone, iPad, or iPod touch - Apple Support do not work because the phone does not appear in Finder. My OS did not come with the Apple Devices app.

I'm in a place where the only way to charge my phone is by plugging the USB cable in to the computer. This flashes the message "Trust this computer?" over and over, and then it quits. The message doesn't stay long enough to click anything, and the phone is not charging. I get this message even with the lid on the computer shut (i.e. asleep). I have tried:

1. Turning off the computer. That seems to make the USB port inactive and no charging takes place.
2. Turning off the phone. It does not charge. If I plug the USB in again, it turns the phone back on.

If this is an intentional design, it is dangerous. There should be a way to charge a phone from a USB port without all the drama. (And yes, I will note that on the page where Apple lets us make suggestions--if indeed this is intentional behaviour.)

Any ideas on how to make this work will be very appreciated!