Until you mentioned it in the next clause, I'd totally forgotten about the literal tiny star powering the ship and thought this was an absolutely wild rationalization for the official length of the ship being a third of the designed length based on the highly-visible bridge and boarding ramp.
I only mentioned the shrinking anomaly from DS9 because Worf said SF could make use of that research for developing Transwarp, and it makes in universe sense (continuity wise) that SF would use that to shrink down a Protostar to something they can effectively 'bottle up' if you will and use for proto-warp (which is Transwarp).
This also sets the Protodrive apart from tech VOY brought back and suggests that SF came up with it all by itself.
The only major problem is that it relies on 2 warp cores to power the proto-warp containtment... for some reason, SF hadn't figured out how to use the Protocore itself to power the whole ship and its own containment - maybe because the energy levels it emits would be too great for SF power transfer systems and at the time it wasn't possible for the power transfer conduits to just 'sip power' from it to power itself constantly), but instead, they can just dump the large surge in power into the Proto-Warp nacelle for a jump).
If the Protostar is effectively a 'baby star' then it would likely produce something like 1% of an actual G type star (which is rated at 385 yottawatts)... so, about 3.85 yottawats.(or 3850000 exawatts - bear in mind that the ENT-D Warp core power output was rated at about 12.7 exawatts).
And if the Proto-core itself onboard the USS Protostar is a shrunk down version of an actual Protostar (which in real life is massive), with the help of that shrinking anomaly which SF likely turned into tech, that would also reduce the power output of the Protostar to about 1% of its original output (if we assume 100x reduction would result in similar reduction in power output)... resulting in the Protocore power output being 38500 exawatts (which is quite a bit more than what the ENT-D capable of, aka, 3000 x more - assuming that the Protostar uses more advanced warp cores, each core could be rated at about 15 exawatts perhaps? So 30 exawatts in total (maybe 40 if we're being really generous in which case the protostar would be 962x more powerful)... that's a far cry for the power transfer conduits to handle in experimental vessel, but I doubt the same would be the case in 10 15 years from 2383 (so round about the time of ST Picard S1, SF should have been able to adjust their power transfer systems to accommodate for something around that level of power - or at least the ability to 'sip' from the protocore - enough so the vessel would have a virtually inexhaustible and ridiculously overpowered power core capable of powering its own containment as well as other systems on board (Which would remove the need for dilithium and M/AM from the picture).
EDIT: my power generation numbers were a bit off.
Protostars would likely have an energy output of 0.1% of a G-Type star (not 1%), therefore, 385 000 exawatts.
If this is further reduced by about 100x, the energy of a protostar in a gravimetric containment would be 3850 exawatts (about 10x less vs what I estimated)... and more 'manageable' for a burst of energy needed for TW - but still out of reach for SF to make use as a general power source (at least in 2383)... but I still maintain that 10-15 years of R&D would have been more than enough time for SF to make headways in power transwer tech to make use of the protocore as a regular power source and power its own containment and other systems onboard.
But reducing a protostar by another 100x would only shrink it to a radii of 34000 km... which is significantly huge.
Don't think something planet sized fits into a proto containment... and if you go down another 100x, you reduce it to 340km... so it would need another reduction of 1000x on top of that to get to 0.034km (or 34 meters in radii...that seems eminently more possible to fit it inside a protowarp containment, but its energy density would fall to about 0.0385 exawatts- well below a single Warp core of the ENT-D... so in this case, SF must have found a way to shrink down a Protostar, but preserve its energy output - or at least a lot of it... so while there would be energy reduction in the protostar from its shrinkage, it might not be proportional/dependent on its size... mainly because it depend on the amount gravimetric energy the thing is able to produce, and this could be something that is more energetic so the reduction curve wouldn't be linear, but far less than - something akin to a tiny black hole if you will which is able to produce huge amounts of energy despite being tiny - and its still deadly).