I think that an engine+battery that is both powerful enough to power the wings, and lightweight enough to be able to take off, is the real challenge.

You simply await the development of nuclear isotope batteries (up to a five-order-of-magnitude improvement on chemical batteries) as a mature technology: https://apps.dtic.mil/dtic/tr/fulltext/u2/a433348.pdf

(And hope that the technology doesn't lead to a new era of arms proliferation with the use of non-fission primaries)

No need — regular hydrocarbons have a high enough specific energy to do the job.

The largest pterosaur, Quetzalcoatlus, had a wingspan of ~10 meters and an estimated mass of 200–250kg [1]. I don’t know how much power they could produce, but it can’t have been more than a few horsepower given they weighed less than a half a horse.

A 30cc petrol motor will easily output 2–3 horsepower, and weighs less than 10 kg. Combine it with wings from a hang glider (similar wingspan, weight ~30kg), and as long as the powertrain isn’t too heavy (compressor + pneumatic artificial muscles?), it seems possible to build something light enough to carry a human.

1. https://en.wikipedia.org/wiki/Quetzalcoatlus

Yep, there was I under the impression that this was more of a marginal endeavour than it really is; I was probably thinking along the lines of human-powered aircraft. I'd imagine that a lot of safety problems and requirements for a very skilled pilot could be reduced in the future with computer control/brain-computer interfaces and exoskeletons.

What are the odds that this went classified and is already working and being used in the field?

I think it's exciting to first get mass production going with as many boring and mundane tasks as possible. Then those more relevant and interesting applications are easier to invent since the base population that can afford these is much larger.