This is actually discussed by the rishonim.
The Itur writes that the correct text is חופה בקידושין, just due to the rules of Hebrew grammar the ב is weak (i.e. a 'vet') and sounds like a vav.
The Rosh writes that we stress the Chupa in order to clarify that the wife is only permitted to the husband after Chupa.
The Mordechai and Taz write that the language ...
The phrasing of the bracha leaves it a bit tricky. It's non-linear.
You prohibited betrothed women from anyone.
But allowed fully-married women to their husbands. When we say fully-married, we mean hey had chupah [unlike "betrothed"] -- of course they also had kidushin previously.
But the stress here is the nisuin effects the permissibility, and ...
One I answer I saw here is:
In the berachah we are referring to the marriage that took place between Hashem (Chatan) and the Jewish people (Kallah) at Sinai. Hashem uprooted the mountain and with the suspended mountain above them He gave them the Luchot — Tablets — with which Eirusin — betrothal — was consummated (see Midrash Rabbah, Shemot ...