With the limited set of Date functions available in AppSheet, this problem requires iteration over a list of dates. So basically, you'll have a list of dates in a table, then you build an expression to count how many dates into this list fall in your criteria: within two dates and excluding weekends and holidays.
The sample app below employs the same concept. It rather calculates future working dates, not the difference between two working dates, but again it is the same concept and you can tweak it easily for your purpose.
Target Workday Calculator - Google Cloud Community
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