PostmarketOS doesn't use the Android codebase, they work on upstreaming devices with a standard Linux kernel, so the opposite. They act mostly the same way as a desktop distribution. They do use the downstream image but mostly as a reference to remove it.
Ubuntu Touch does use the Android vendor images though through the libhybris compatibility layer, that's why they have some good compatibility, if the phone has a lineageos image, there's a good chance that it'll work with Ubuntu Touch.
The downside of that is the same as Lineageos, they are stuck on whatever kernel the device shipped with and it can be ancient.
> So you need some way to run Android apps... which is totally possible, but at that point why not just use Android?
Perhaps for reasons like this: https://news.ycombinator.com/item?id=26639261