That’s all well and good, but it sure makes it hard to be an interested layperson.
I note there is a broader classification called “mammaliformes”, which includes the mammal ancestor and the clade to which Castorocauda belongs. So one could argue it’s a choice of which word is used where.
But yes, I see your point.
The confusion comes in with things like saying birds are “reptiles”. You’re leaving a lot of laypeople in the dust. But I suppose it’s no different than the IAU declaring that Pluto is no longer a planet.