Excitations can carry dynamical properties. For example, jerk a rope once, and you will see a wave travel down the rope, which carries energy and momentum. If you give the rope a quick twist, the wave carries angular momentum.

I have the same problem with this analogy. The rope itself is just excitations of a quantum field. It feels like there is very little underpinning everything.

It simply turns out that, in order to be a stable excitation of the vacuum, an electron must have all the properties of an electron.

I've not yet encountered an experimentally-testable explanation that goes deeper than that.