Running Haiku from USB only / Laptop with USB stick as hard drive

I don’t know how well Haiku runs on current Framework generations but disagree it is what the OP is looking for. To my ears the proposal sounds like the MNT Reform. This uses compute modules based around single board computers.

Currently it only uses ARM based processors. Whilst Haiku’s ARM port continues to evolve, and there is no reason they can’t introduce a RISC-V compute module (on which Haiku is more advanced), the Reform also runs Genode/Sculpt.

Not only is this an “OS Framework” that can be used to build - indeed specialises in - minimal host for virtual machines to run diverse OS, it is also the basis of a fascinating project called Haiku on Genode which has been discussed here in the past. I have also speculated myself as to whether I would benefit from running Haiku virtualised on Sculpt in this post.

Only problem with the Reform is it is a hand-built product with price to match, but no reason why cheaper materials and mass producing can’t be applied (MNT is very strongly open source hardware).