You have a small bit of confusion here.
Let's say, just for a moment, that Archy actually is a 'transitional' form. Ok, what would you call it?
There is no taxonomic term for something that isn't a bird but has feathers. Archy can be called a bird because it has several bird specific features, most notably feathers. Archy can be called a reptile because it has very clear reptile features. When it has both there is no name for it.
So now the taxonomists start to argue. It's a bird! It's a reptile! It's a plane! The name isn't the point.
If you want it to be a bird, then it is a bird with reptile features. If you want it to be a reptile then it is a reptile with bird features. It has
both. This is exactly as you would expect in a transitional.