You're confused. Linnaeus lived 3 centuries ago. Science and technology has kind of advanced since then don't you think? It's 2022, not 1752.

None of the arbitrary superficial morphological traits you listed matter. Traits can appear or disappear in different groups. What you are saying is the same thing as trying to say that a penguin isn't really a bird because penguins swim and they can't fly, or that a bat isn't a mammal, because bats fly and have special traits.

There are non-avian reptiles alive today (such as alligators? that are more closely related to birds than to other reptiles (such as turtles) .... because birds are also reptiles...and also birds. The same way that a human is a human, and also a primate, and also a mammal, and also a tetrapod. And you can't go and then say "but bats aren't mammals".

It' not just "bird or reptile".

Have a great day. Take care.