Since you are indexing private_subnet with a numeric value, it must be a series of values like a list or tuple. The index for a series is a number, there is no “word” equivalent.
If you need to find a value in the series via some other attribute, you can use a for expression to iterate through the series to find the value you need. For example, assuming values here is a list of strings, it might look like:
value = one([for v in local.values : v if v == "desired" ])