I'm not going to argue with your clear reference but I will reference this article: https://askabiologist.asu.edu/questions/birds-dinosaurs-rept... which adds a bit of useful context.

"So a reptile is any animal descended from the original group called reptiles. Both birds and mammals share ancestors sometimes referred to as reptile-like animals (Reptiliomorpha), but it's not very common for people to talk about mammals as reptiles."

That’s because mammals aren’t reptiles:

Mammals are from Synapsids[0] and dinosaurs (and modern reptiles) are from Sauropsida[1] — with the commonality being that amphibians split off first [2]. We can draw disjoint clades, which we cannot do for birds and dinosaurs. Beyond that, you’re just talking about tetrapods in general [3]. Reptiliomorpha has multiple names, precisely due to this — eg, pan-amniota.

0 - https://en.wikipedia.org/wiki/Synapsid

1 - https://en.wikipedia.org/wiki/Sauropsida

2 - https://en.wikipedia.org/wiki/Amniote

3 - https://en.wikipedia.org/wiki/Tetrapod