I’ve seen contrails that looked a lot like this over my house before, and I’m certainly not in a location anyone would choose to fly a top secret aircraft over in broad daylight. Plus a pulse detonation engine on a high speed aircraft would be pulsing many thousands of times a minute, which means large spaces between puffs doesn’t really make any sense.
Anyway my experience with the PDE conspiracy theories is that the people spouting them usually have no clue what the actual advantages of PDE are. Mainly, people seem to always equate PDE with high speed and super secret awesomeness, when in reality its main advantage is high thermal efficiency. That means PDE technology is more likely to appear in a power plant or a commercial airliner using hybrid engine then some elite military spy plane program. If the military wanted to go fast in secret they’d just make a modern D-21 with a ramjet and call it a day.