Bumper movement water damage?

That discoloration is nothing to worry about necessarily IMO. Of course, all of these movements are old, so you really can't judge them from a photo. Always assume they will need servicing.

I would be more concerned by why there doesn't appear to be a steel pivot in the central ruby bearing for the rotor.

Water damage is usually more immediately evident with RUST showing on the steel parts. A bit of tarnish is not a concern. But if the rotor post is broken, that is a cause for concern.

This is a watch forum myth...

The cleaning solutions used have nothing to do with this. No commercial cleaning solution will damage the plating, so suggesting there is a "wrong" or "right" cleaning solution for cleaning these parts is just not true. It's not like Omega approves a cleaning solution specifically for these calibers - they just use the same solutions that most companies use, and that Omega uses for all their watches.

The fact is, this plating just wasn't done very well to begin with - watchmakers who work on vintage Omega know this well, the plating comes off very easily. If there's anything contributing to the plating coming off with respect to cleaning, it would be related to using ultrasonic - either too strong or for too long. But even when cleaned in a regular agitation cleaning machine with no ultrasonic, the plating will sometimes flake off on these movements.

The watch in question has very little in the way of plating missing, just some on the rotor and that could be from wear.