It's not always obvious but the bit that is clear is it's hard to delineate "dad is working so don't interrupt him" for on-call incidents etc vs "dad is looking at cat videos". They look the same and it's pretty clearly confusing because it's a malleable boundary.

In terms of attention I actually find it pretty easy to identify their cues even when on my phone. It's more of a general feel of how much I've played with them vs solo play and when they want to hang out they will walk over and make it clear. Plus you are always watching them.

Moreso they are interested in the phone because we are but I don't necessary sense frustration. Especially if you are "attentive" in that you are willing to context switch back to your kids immediately, I think they see it as another "thing" like a toy or some distraction outside.