Maybe the 4ET50 is simpler than a modern automatic transmission, I just have a real hard time wrapping my head around how it works.
Here's a great teardown video to see how it works.
Very few moving parts, they're all gear-gear (no belts or chains to wear out) and two clutches, which engage @ 0rpm (virtually no wear)
In terms of reliability of moving parts, it's right at the top. The only question mark is that bearing cage.
As to how those gears are actually put in motion, you just need to focus on the clutches.
One motor doing all the work.
engage clutch #1 - second motor helps out.
if engine is on, engage clutch #2 and one motor is making power, one is putting power to the wheels.
Engage clutch #1 & #2 and the engine can help both motors drive the wheels as the driveshaft is indirectly connected to the gears to the wheel (through the clutch to rotor of the small motor and the clutch to the main drive)
From there everything else is controlled electrically - if engine produces too much power, siphon some out from one of the motors and store in the battery. If it's not producing enough, add some in via one of the motors.
That's how you get essentially infinite "gear ratios" to get max efficiency from the engine without actually shifting a gear set.