Good on you for running Haiku! Whilst it has become increasingly popular as of late, with an increasingly fleshed-out library of native software, it also strikes me as likely a good companion for the little Framework with its smaller screen and lower power. The OS is so elegant, both in terms of GUI and underlying software architecture, it should be quite efficient to operate on the small format device.
Note there is a Haiku thread on the Framework forum already! Of course Haiku is not the only option for those looking for something not based on linux or windows…
Sculpt. Privacy focussed operating system from Germany. The developer, Genode labs, have a Framework in their testing fleet. Another OS well suited to smaller screened devices, it works on the MNT Pocket Reform and Pinephone.
9Front. Based on Plan9, Bell labs successor to Unix. It apparently has been made to work with some models of Framework: has anybody tried it on the 12” model?
There is also the BSDs, perhaps somebody can advise how well they work?