A main sequence type star like our own emits 384.6 Yottawats of energy every second (that's 384.6 MILLION Exawatts per second).
Ent-D Warp core was rated at 12.7 Exawatts per unspecified time frame - but the script indicated that Data was supposed to say ' per second' in 'True Q' (so, yeah, the Enterrprise - D M/AM power source doesn't even come close to a main sequence star in terms of energy production... and even if a 'baby star' was a more accurate term and if it emitted just about 10 000 exawatts per second or, 100 000 or even 1 million exawatts per second, that would still vastly surpass Ent-D Warp core power generation while considered a 'baby star' - at least in power generation terms).
Also, the ENT-D Warp engines were capable of reaching and sustaining Warp 9.6 mostly (Voyager was only able to sustain Warp 9.75 for 12 hours - not 9.975).
Jankom Pog indicated that a single Warp core on the Protostar could take them to Warp 9... suggesting a slightly less powerful or equally powerful Warp core as on the Ent-D... times two of course.
As for whether we are looking at ignorance of scale... well, it depends.
A protostar is massive (to say its 'much' larger than a star would be an understatement actually), but in terms of energy output doesn't come close to a main sequence star at all (but it DOES produce energy and radiation).
Fusion can still occur in a Protostar when it reaches a certain point in its transition to becoming a main sequence star... so its possible that SF found a way to create or harness a Protostar, then shrink it using a tech they made from encountering that shrinking anomaly from 'one small ship' in Ds9 without compromizing on its energy/radiation production (which could be potentially enhanced with subspace properties) or some other technology or techniques they developed (maybe creating an artiticial universe... and instead of doing that, they created a Protostar), and trapped it in a specific state so they can use it (or just its specific radiation) for jumping to Transwarp - it could be in a stage of becoming an actual star, which would mean that its still technically a Protostar, but with an energy output vastly surpassing that what you can get from matter/antimatter reactions that are enhanced with subspace technology.
The containment field which keeps the Protostar in place is a massive power drain... and given the gravimetric distortions emitted by black holes and stars (Protostars included), you'd have to be able to contain massive amounts of gravity (which is probably why its called a 'Protostar gravimetric containment').
This also begs a question: what keeps the Protostar in place when the ship is powered off?
Aka, what happens to it and/or where does it go when there is no power through the ship?
The most likely 'Trek' explanation would be that if you don't 'feed' it, then it won't produce energy, meaning it goes dormant until you feed it matter [much like a black hole]... or it just vanishes into subpspace and re-emerges when the ship is active (which seems conveniently unlikely).
Containing a stellar phenomenon like that... it shouldn't be possible for a ship to be 'switched off' at any time if you wanted to keep it onboard.
It would have to be similar to a Forced Quantum Singularity used by the Romulans. Meaning, once its switched on, it can't be turned off... same principles would apply to a Protostar or even a Main sequence star... unless the Protostar is created and snuffed out every single time a ship is powered on or off (which doesn't seem like it would be possible - it just seems more likely the Protostar goes out of phase or something to that effect and just 'appears' inside the containment when the ship is switched on).
Although fusion reactors are basically like mini suns... its a matter of INITIATING fusion reaction (so, emulating what happens inside a star in a controlled fashion).
So, its possible they don't have an actual protostar but are tapping into 'baby star' energy generation potential by triggering a protostar reaction for generating energy and radiation far surpassing what can be produced with 24th century fusion reactors and antimatter.
Its a cool concept, but we're still in early days and we have no detailed explanation behind how the UFP managed to do all of this or if the classification for a 'Protostar' is technically accurate.
But to say its 'solar powered'... eh... since a Protostar is NOT technically a main sequence star, then no?
Its somewhere before that.