How to counti cells that are not blank but ignoring formulas

If formulae are returning blanks properly, then there should be no issue.

Attach a sample workbook for troubleshooting, please.

Should be like this: =SUMPRODUCT(--($A$1:$A$12=$B$1:$B$12))

in terms of COUNTIFS, specifically, it all rather depends on what B is returning -- if text

=COUNTIFS($A$1:$A$100,"",$B$1:$B$100,"?*)

the use of ? will account for any null strings generated by formulae.

if you're returning numbers in Col B use a number based test, e.g.:

=COUNTIFS($A$1:$A$100,"",$B$1:$B$100,">-9.99E+307")

if you need to account for both data types you would need to combine the 2 COUNTIFS, e.g.

=SUM(COUNTIFS($A$1:$A$100,"",$B$1:$B$100,{"?*",">-9.99E+307"}))

edit: I misread your criteria re: Column A, i.e. non-blank constants as opposed blank constants, but I suspect you can amend the above examples to account for your real-life requirements.