The short answer is "No". Perhaps there is a little confusion at work here, because this verse is embedded in one of the Aramaic passages found in the (otherwise) Hebrew Bible: it is not in Hebrew.1
The "-ah" ending that makes this look like "prophetess" (if the word was in Hebrew), is in fact the Aramaic definite article, = "the". (See heading 2.2, bullet #2 in the link, above.) There is no question of Haggai being a woman.
For corroboration, see the very last entry on p. 1101 of Brown, Driver and Briggs, A Hebrew and English Lexicon of the Old Testament (it comes from the Aramaic section at the end), or the very last line of p. 868 (with the entry itself on the next page) of Marcus Jastrow's Dictionary of Targumim, Talmud and Midrashic Literature.
For convenience, here is the whole BDB entry for the word(s) in question:
Also, bonus citation, this the corresponding entry from Ludwig Koehler, Walter Baumgartner and J.J. Stamm (eds), The Hebrew and Aramaic Lexicon of the Old Testament:
The little "dagger" (†) symbol in both entries is the standard symbol in these lexica that means "all known occurrences cited in this entry".
Neither of these authoritative lexica makes any reference to "prophetess". I hope that helps.
(One moral of this story: use "Strongs" with extreme caution, and especially in the absence of knowledge of the languages themselves.)
Postscript: for comparison, this is the Jastrow entry (linked above) indicating what the "prophetess" (feminine) form in Aramaic would look like:
(Note that the references provided as examples for the forms circled in red come from the Targumim - Aramaic translations of the Hebrew scriptures.)
- I don't know why the Biblehub (OP's link) has the mark-up it does. All the related terms of interest for this question are found in the entry for Strongs #5013 - in left column, note reference to "Aramaic"; the three terms at the top of the right column are found in Ezra 5:1. (N.b. This entry, #5013, refers to an Aramaic word: it should not be confused with #5031 which is a Hebrew word!)
As a comment on the Question notes, "Ketiv/Qere" is also a factor, not once, but twice in fact: once each for the descriptors given for Haggai and Zechariah!