In short, thermoplastic composites are "like fiberglass and carbon fiber, but using thermoplastics instead of thermosets".
I have found polycaprolactone to be an enormously productive medium to create parts out of. If there were something akin to a "hobbyist-accessible polycaprolactone with impregnated fibers", that could be really exciting.
Fibre-reinforced thermosets are always applied to a rigid form, which might make prototyping difficult. However, maybe it would be possible to use the iterative refinement technique that I use with plain thermoplastic?
Bits of information I've been able to gather:
There's been a lot of research around these materials in the last five years, but the vast majority of information about these is either 1) scholarly research, or 2) sales materials from bulk-material companies, trying to convince manufacturers to use their products. The key thing is — I haven't seen any manufacturers building real products with it.
If manufacturers aren't currently building anything with it, then hobbyist information is going to be virtually nonexistent. This means that any hobbyist that uses it will need to do a lot of experimentation to figure out what manufacturing-level composites might transfer and work well for the hobbyist community.
I'm going to classify this as "pretty cool from a material science perspective, but currently too untested at the engineering level for me to dig into" because it's still at a very high risk of being a technology that fails, turns out to be useless, or that decades more research is needed before it can be used in practical manufacturing.
This will be worth re-evaluating in 5 years (it's currently 2023), but right now it feels way too new for hobbyist use.