It's hard to believe the algorithms are that wild. They can't be blocking Russian-related vendors, can they?
Nope; asking for a balalaika returns an offer for a violin kit, followed by several for balalaika prima (and that blue kazoo again, and a ukelele). I guess the domra is just not weird enough for quick recognition, so it isn't so popular. Or that sponsored offers are shoved in anyplace they might be remotely relevant. But I still don't understand the blood pressure meters. Maybe they figure you'll need them after the interminable search for what you want.
UPDATE: "domra folk musical instrument" finds one, mixed in with with the kalimba and flute and wave bead ocean drum.