OK. So I finally got my hardware and have done some testing. Unfortunately to no success.
I bought two adapters, a usb-c → DVI adapter from Cable Matters and a DP → 2x HDMI from Cables to Go.
The usb-c → DVI adapter seems to work fine.
It took a while to test the DP → 2x HDMI adapter, and I’ve concluded that the DP port in my Framework is faulty. Testing was complicated by the fact that the Framework is the only computer in the house with a DP port.
There’s another possiblity, that Fedora 37 is the problem. I haven’t made the time to boot to another OS and test that, but that’s next.