eg, you could be running (say) 3 or 4 primary applications at the same time. Which one gets to use the FPGA pieces, or are they re-written every time, on every context switch? ;)

Re-writing them on every context switch sounds extremely unlikely, so it'd be more some kind of resource locking thing instead. Which could mean that FPGA-using applications at least start out being fairly niche, as only one could run "per core" or something.

Maybe dedicated cores per application instead or something?