(Author here)

There's no built-in mode for constant power. (Nor could there be, on the original Bike that I have, as the resistance control is manual.)

The new one might have it.

At a hardware level I'm not sure how well it would work. Out of the box, the tablet only queries the bike for cadence/power/resistance every 100ms, one query at a time in round robin, so your power reading is only coming every 300ms. However, the bike responds to queries much faster - on the order of 200-300us (https://ihaque.org/posts/2020/12/26/pelomon-part-ii-emulatin...), so an external device could certainly ask for updates faster. I'm not sure how rapidly the micro on the bike itself actually updates its own measurements and what ultimate time resolution is possible.