Why won’t my iPhone 13 connect to my 7th gen iPad via bluetooth?

That is because the iPhone and iPad are not designed to pair via Bluetooth. What is it that you are trying to accomplish? While there are tasks that can be done via Bluetooth, most just require that Bluetooth be turned on for both devices, not actually paired.

And you should get anything else that would be connected. I see the same thing, and when my hearing aids are turned on and in use, that will appear, but will not if they are not turned on. The same with my AirPods Pro. As soon as I open the case to pair them with my iPhone for use, that appears in the widget too. In the battery widget for my iPad, my Pencil will appear too.

What other devices are you expecting to see there? Not everything can report that information.