Pico different behaviour on Battery

Yes, deep sleep would be disabled - I'd hope the normal sleep shouldn't cause you any problems with timing though as it still keeps the high speed clock running (including the SysTick timer - why the sleep indicator should blink ~4 times a second).

Have you tried attaching LEDs to each of the TTL outputs from the sensors while it's all in your circuit? It might help to narrow down whether both sensors actually are firing at the same time, or if it is a problem with Espruino. I guess you could also try just replacing both sensors with switches to see if you can replicate it?

I haven't seen this kind of thing before, so I'm more inclined to think it's some electrical issue (could be noise on the 3.3v line from Espruino suddenly doing some computation and turning on an LED?)

On an entirely unrelated note... ghost code

Is it possible that you unchecked Reset before send in the Web IDE Settings? That could cause you a whole world of pain, and may also explain some of the issues you're having?

You can check what code is currently in the Pico by typing dump() in the left hand side. It's not perfect as it has to reconstruct some things, but it should give you an idea whether you have what you expect or not.