There is no single word that is really commonly used. Some might be accurate, but they are so uncommon as to sound strange to some people.
I would say the most accessible single word is betrothed:
: engaged to be married a betrothed couple
// … clasped hands, signifying the bond between betrothed men and women …
— Mary Feilden
// For three years she and Emilio Estevez were an item and were even betrothed for a time.
— People Weekly
: the person to whom someone is engaged to be married
// … she put on her grey silk gown and her cherry coloured ribbon with as much care as if she had been herself the betrothed.
— George Eliot
Used as a noun, the betrothed can refer to a single such person, a couple, or multiple people.
In terms of commonality, Google Books Ngram Viewer shows that the betrothed is more common than the espoused, the affianced, or the postulants (and note that espouse also has the second sense of supporting a cause, meaning its engaged sense is even less common):
Although the betrothed is arguably the most common and least esoteric of possible phrases with an article and a noun, I'd say it can't be as natural as just using the bride and groom in the first place (or the brides or the grooms in the case of same-sex marriages), or something like the happy couple where the context is known: