I think it's "always" not "often", as "vestimentum/vestimenta" don't obey to the English rule about "clothes" being an uncountable. In French, where "vêtement" has the same status than in Latin, a normal countable word, you won't never consider that "le vêtement" is the same as "les vêtements", it's not possible.
Clothes, in fact, is not countable. "I have three clothes in the closet" doesn't make sense. You can, however, say, "I have three pieces of clothing in the closet." It's the same as the word food. "Yes, waiter, I'd like three foods please" would get you strange looks, but "I'd like three [certain type of] meals" is much more reasonable.
American English differentiates between "closet" and "wardrobe/armoire".
A closet is assumed to be built into the wall, a small room with clothing storage. These can be very small - my house was built in 1915 and the closets are only about 10 inches deep and barely wider than the doorframe - or quite large and referred to as "walk in closets".
A wardrobe or armoire (most regions of the US tend to use the French, not British term) is a separate piece of furniture. It is used in rooms that have no built-in closets or where they are too small to be usable (like my house).
Legally, in most US cities, a room must include at least one built-in closet to be considered a bedroom.
That last comment is interesting. To judge from the plethora of television programmes about buying and refitting houses, most UK house buyers are busy ripping out what we would call built-in wardrobes to make the rooms appear bigger, and replacing them with free-standing wardrobes, which miraculously have no discernible effect on the room size, or so the presenters would have you believe.
I suppose we could make ripping out built-in wardrobes illegal to match up with the USA, but I suspect there would be an uproar. You have to admit, it's almost as daft as making crossing the road illegal.
The difficulty is that in English we rarely use the word garment in conversation. I expect to hear it from sales people. The alternatives are a bit clunky. Article of clothing? Item of clothing? Not really doing it for me.
"Is the garment in the closet?". Who would say that? An investigating police officer? I just don't know. It is an awkward gap in the English language. We usually fill it by specifying the item in question. "Is the shirt in the closet?"
I definitely don't like the word garment here as it is not in fact what one would say in this context in English; perhaps in Victorian times. So I've looked over this thread and found no satisfaction. Certainly piece of clothing is worse.
Best seems to me
Is the clothing in the closet?
Are the clothes in the closet?
This presupposes it is already understood what article of clothing one is looking for and the specific designation is not being repeated.
Clothes/clothing are singular and plural; clothes takes a plural verb, clothing a singular verb, regardless of actual number.
Other things to try would be suit, robe, dress. Since clothing styles have changed over the years it's unclear what should be accepted. And it's unclear what is accepted so I suppose I'll need to experiment.
I suppose one could also use vestment though that is pushing it.
vestimenta, as you know. but it seems you are looking for something more. given the nature of languages there is likely more than one word and/or expression for one thing. Latdict interestingly has more than several words but does NOT include vestimenta or singular vestimentum.