I think troosers is a different word. Trews exists in Scots with a very specific meaning of a certain type of tartan trousers.
Triubhas just translates trews according to AFB but Dwelly says
-ais, -an, sm Trousers, pantaloons. 2 Ancient article of Highland dress, generally made of tartan cloth and consisting of trousers and stockings in one piece, trews. 3(Fionn) Roe of a fish — prov. (—Argyll & West of Inverness-shire — AH).
The English word trousers is thought to come from Middle Irish triubhas but it could equally well be Gaelic with the same spelling (see Dwelly).
Breeks/breeches comes from Gaelic briogais or Irish brigis.
These two words are singular, as is reasonable for a single article of clothing. The s is not a plural marker in these languages (as we all know by now) - it appears to be there by chance - but it appears that when these words came into English, they got mistaken for plurals, helped by the fact that they refer to things that have pair-like quality since they cover a pair of legs. This may well be the origin of all the plural nouns and pair-of-x phrases that are used.
They have introduced plurals in -(e)an first as they are commonest and simplest. As in Swedish there are other ways as well including vowel changes (which I assume are used in Swedish). But the one type of plural we don't have is adding an -s. This does not actually mean that it is singular. It could be (but isn't) the plural of *briogas.
Meanings evolve. triubhas/trews were originally close fitting on the leg. Only worn by people who had a horse to sit on (high status). Nowadays in Scotland triubhas/trews is generally recognised as tartan trousers (looser fitting). BTW Americans calling trousers pants often causes hilarity. American to Scot 'I like your pants' Scot to American 'Oh I must have a hole in my trousers!'
Yes, they are not very consistent. Sometimes they only accept the form close to the Gaelic (for example to 'take' a drink) when it is not what would be said in standard British or American English, and sometimes they do not accept the similar form, even though it is valid (even if not common as in this case). Since many people will find the similarity with breeches help them remember the Gaelic, and since the word has no meaning which could confuse the learner or that suggests the learner has misunderstood, I think they should simply accept both in these situations. This is a course in Gaelic, not English, and I think they should generally accept any form that meets the two conditions above, with one important caveat. We cannot expect them to think of every obscure word that people might think of, but when there is an obvious cognate, as here, or a translation that lots of people would use naturally, then it should be accepted if it meets these criteria, regardless of whether it meets any particular (and hence restrictive) criterion for what is English.