Google Sheets Pattern Matching/RegEx for COUNTIF

This is a really big hammer for a problem like yours, but you can use QUERY to do something like this:

=QUERY(E9:E13, "select count(E) where E matches '50-03[123][012]' label count(E) ''")

The label bit is to prevent QUERY from adding an automatic header to the count() column.

The nice thing about this approach is that you can pull in other columns, too. Say that over in column H, you have a number of orders for each part. Then, you can take two cells and show both the count of parts and the sum of orders:

=QUERY(E9:H13, "select count(E), sum(H) where E matches '50-03[123][012]' label count(E) '', sum(H) ''")

_{I routinely find this question on $searchEngine and fail to notice that I linked another question with a similar problem and other relevant answers.}

As you identified and Wiktor mentioned COUNTIF only supports wildcards.

There are many ways to do what you want though, to name but 2

=ArrayFormula(SUM(--REGEXMATCH(E9:E13, "50-03[123][012]*")))

=COUNTA(FILTER(E9:E13, REGEXMATCH(E9:E13, "50-03[123][012]*")))