The linux synaptics driver also supports other brands, I know alps works.
But it looks like Framework uses a PixArt PCT3854QR. So I think you may be out of luck.
Also, linux touchpad drivers can just be crap. And I say this as someone who loves linux and has used it on desktop for over 10 years. Though, I find synaptics to be fine, for the little I use my touchpad.