The condition that you're asking about is called in the professional terminology: "madarosis" (but see the picture that I attached). As many proffessional books states, it's common in hypothyroidism, and they don't say it about hyperthyroidism. Then it make sense that it's not common in hyperthyroidism. But in medicine always can be exceptions.
Regarding to the side effect of carbimazole, according to this source which rely on FDA report, there is no such side effect of carbimazole, and obviously it is not common as well.
"Could Methimazole cause Madarosis? - from FDA reports
There is no Madarosis reported by people who take Methimazole yet. We
study 2,148 people who have side effects while taking Methimazole from
FDA. Find out below who they are, when they have Madarosis and more.
1) Thyroid Disorders with Cutaneous Manifestations (p.129)
2) Illustrated Synopsis of Dermatology & Sexually Transmitted Diseases (p.384)