Is it linguistically and doctrinally correct to use the word "أديانهم" (their religions) in the aforementioned supplication, and is it permissible to use its plural form with the intention of conjoining it with the plural "أصحابي" (my companions) without intending multiplicity?

There is no problem, linguistically or legally (according to Islamic law), with the validity of using the word "their religions" (أديانهم), nor is this considered a doubt about the unity of the religion of Muslims. Its use has been mentioned in prophetic traditions (Hadith (definition)) to denote a person's religion, as in his (peace be upon him) saying: "People are tested according to their religions." Its use has also been widespread among scholars in their writings. As for mentioning a specific number with a remembrance (dhikr), this does not mean repeating the word by the number of the remembrance; rather, it is an indication of the great reward of that remembrance. So, the saying "Subhan Allah (Glory be to Allah) as many as His creation" is not considered a repetition of the words "Subhan Allah" by the number of His creation; instead, it is a single glorification that warrants this immense reward.