Thank you, too.

Yeah, it's a little confusing. For the moment I will not modify any cross again, let's see if it is clarified in the future.
Also note how in the wiki is used different types of crossing=* with the crossing_ref=*
crossing=*#Examples

Theoretically it can be an alternative but I understand that the traffic signals are always more important than the floor markings, so crossing=traffic_signals will be better.
I don't understand a lot the other case you expose. If I get what you say, I think you are right. It would be crossing=marked, and maybe adding crossing_ref=zebra? I don't know about legal implications of this tag, but I think it doesn't modify anything, it serves to describe better the crossing.

Wouldn't that be crossing=traffic_signals?
And if there is zebra markins complement it with the crossing_ref=zebra?

Hi, I normally used to change crossing=zebra for crossing=marked as iD suggests plus cossing_ref=zebra to not loss information.
Also, note that in a lot of places people used to tag as crossing=zebra even there is no zebra markings.
I think the crossing=marked + crossing_ref=zebra schema is more similar to other tags OSM uses.
I agree that there is still no clearly decided implementation. So maybe I'm wrong.