It all makes a lot more sense, at least to me, when you realize that the “electron cloud” configurations that we see (1s, 2s, 2p, etc) are identical to patterns produced by standing waves. Which shouldn’t be surprising, since, quantum mechanics is just an offshoot of standard wave mechanics.
The electrons can cross paths, collaborate, be “shared”, etc, because we are talking about how waves interact, and not really about how some tiny particles interact. The difference between particle-waves and say, ocean waves, is that when the particle-waves interact, they can influence the position of what is producing the wave. So, the center of the wave (what we would think of as the electron “particle”) can be moved by the interactions of the waves that “particle” is emitting.
This allows phenomena like feedback loops to develop, and all the complex interactions of particles, atoms, molecules can develop from there. The waves naturally tend towards harmonious, stable configurations to oscillate with a minimum of interference, and while attempting to reach those configurations, they move their “particles” along with them into the complex configurations that we know.
Yes, thinking about an electrons in terms of a cloud of probability can be very helpful in many ways.