I think the volume of air produced would be more of a limiting factor than the pressure (function of head height), but I haven’t done any type of calculations on it. I don’t actually know how to calculate a flow rate from a trompe, but I assume it’s based on sizing (diameter) and volume of water through the system.

For your paddle wheel idea, I saw online where someone tried a paddle wheel to turn the crankshaft on a small engine with an air hose screwed into the spark plug hole. I would think you would either need a big motor or some very fast water for that to work well, but it’s an idea that doesn’t use electricity so I thought that was interesting.