Are special recipes needed to preserve using a pressure canner?
The trusted recipes you get from, e.g., a university extension are tested to make sure that they actually heat through entirely and for long enough to destroy bacterial spores, in particular botulism (but also a few more less deadly ones).

In water bath canning, you're using acidity (primarily) to make sure botulism can not grow from the spores, which are not destroyed by boiling water canning. The inside of the jar isn't actually sterile.

In pressure canning, you're actually destroying the spores. So you can can things where the bacteria could otherwise grow—because the inside of the jar is sterile.

Destroying the spores requires reaching a particular temperature for a long enough duration. If you don't do that, once the food cools down, the spores will germinate. A very bad outcome.

The key thing is that (as always) the outside of whatever you're canning heats first. The heat then transfers in towards the center. But the rate of heat transfer can vary greatly depending on what it is.

If heat transfers slowly, you have to pressure cook longer. If heat transfers quickly, you don't have to cook as long. Generally, you'd like to process for as short a time as possible, to preserve texture and flavor.

When developing a safe canning recipe, multiple batches are prepared and each is canned with special equipment that allows measuring the temperature at various points inside the jar, during the pressure cooking. They time how long it takes for all the points to reach safety, and of course repeat this multiple times. That's ultimately where the processing time comes from.