I think the input Date in the live app is different from what you have in the editor and is not a value that can be parsed.
The weweb date element uses dayjs (from what I see on its public repo). Dayjs formats invalid dates with the string ‘Invalid Date’ like the one you are getting.
The problem should be the bound value assigned to the input Date, double check that is a valid value:
string (check string docs for standard formatting).