You iCloud account is your identity. When you choose to share things directly from your phone, you are choosing to share that identity. How else can another iPhone verify you?
There is no information leak. This is a clickbait title combined with a 'Well, duh' moment.
With that said I agree with you that it’s an intuitive and non-serious disclosure, but it appears some disagree.
Which it to say, it sounds like you only get partial information about the sender prior to identifying yourself and establishing a direct connection. So you cannot passively identify the exact phone number of an unknown sender.
The "short identity hash" itself it says is "created based on the email addresses and phone numbers associated with the user’s Apple ID", though I have to assume that it's independently hashing each piece of info because if you hash the whole set, then the receiver would have to know the whole set, which would be a problem (my device knows more email addresses for me than any of my friends do).
https://github.com/hexway/apple_bleee/blob/master/hash2phone...
If visibility is set to everyone then your phone will identify itself using its phone number so people know which device is yours and can click to share with it.