Like nearly every time, empty string and 0 for integers can be treated the same as "no value" if you think about it. Are you sending data or sending opinions? Usually to force a choice, you would make a enum or a one-of where the zero-value means the client has forgotten to set it and it can be modelled as a api error. Whether the value was actually on the wire or not is not really that important.

Not really one domain in particular, just internal services in general. In many cases, the field is intended to be required in the first place. If not, surprisingly 0 isn't a real answer a lot of the time, so it means none or default: any kind of numeric ID that starts at 1 (like ticket numbers), TTLs, error codes, enums (0 is always UNKNOWN). Similarly with empty strings.

I have a hard time thinking of places I really need both 0 and none. The only example that comes to mind is building room numbers, in some room search message where we wanted null to mean wildcard. In those cases, it's not hard to wrap it in a message. Probably the best argument for optionals is when you have a lot of boolean request options where null means default, but even then I prefer instead naming them such that the defaults are all false, since that's clearer anyway.

It did take some getting used to and caused some downstream changes to how we design APIs. I think we're better for it because the whole null vs 0 thing can be tedious and error-prone, but it's very opinionated.