Does anyone know if I could build my own adapter board for a Pi 3 Model A+? Apologies if this has been asked before.

An adapter to use on a Turing Pi system? There is a huge difference between say a CM4 and a Raspberry Pi 4B. Sure they have the same processor and RAM, but the form factor is totally different. The CM4 has pins on the bottom and it is designed to go on a board.

Yeah, but an adapter could exist. There was some discussion lately over #754950670175436848 iirc, and someone wants to make one for their KS project

Yes, they are talking about a RPI. So they are going to make a board for what, the GPIO pins?

Sadly it won't work for RPi this way. More functions than just GPIO would have to be exposed, as in CM modules in general.

You can't expose the other functions as they were not intended to be exposed on anything but the RPI. The CM4 was designed so that the carrier board would provide what is physically missing from a CM4. At the end of the day the RPI is designed to be a self contained system. The CM4 was designed to support a number of different form factors and that a carrier board would be needed for whatever the task at hand was and it would expose the functions that were needed. The CM4 was really more designed for integrators. If you need wireless you can get CM4's with that. If you don't want wired Ethernet, then the carrier board doesn't have to support it. The PCIE interface can be used for many different things. For someone making a commercial product, the CM4 makes a lot more sense that a Raspberry Pi 4B would. A good example the Pi KVM. The V3 variant was a HAT that went on a RPI. Now they are making a new variant using a CM4 module.