I started hearing leashing sounds both randomly as well as on login, so I realized that it happens when the wandering trader and their llamas are spawned in. so I quickly added an instanceof PlayerEntity check (with a bytecode editor for personal use) inside:

} else if (!(newHoldingEntity instanceof LeashKnotEntity)) {

(so it wouldn't jump into the next case) in ClientPlayNetworkHandlerMixin.onEntityAttachSound. I tested it before and after with commands to test if it's fixed, which was the case. This might be a good addition to the mod

here are my test commands to reproduce (despawn delay is required due to MC-210224)
/summon wandering_trader ~ ~ ~ {UUID:[I;2,2,2,2],DespawnDelay:2147483647}
/summon trader_llama ~ ~ ~ {Leashed:1b,Leash:{UUID:[I;2,2,2,2]}}