I have some trouble while reading a proof of a lemma in the book "Pseudo-reductive group" (Conrad - Gabber - Prasad). Here is the lemma:

Lemma C.4.4. Let $G$ be a group scheme locally of finite type over a field $k$, $T$ is a maximal $k$-torus in $G$ and $K/k$ an extension field. If $G$ is smooth or commutative, or if $K/k$ is a separable extension, then $T_{K}$ is a maximal $K$-torus in $G_{K}$.

In the proof, the authors wrote:

Suppose $G$ is connected and commutative. Any $k_{s}$-torus in $G_{k_{s}}$ has a $\text{Gal}(k_{s}/k)$-orbit consisting of finitely many $k_{s}$-tori, so by commutativity the collectively generate a $\text{Gal}(k_{s}/k)$-stable $k_{s}$-subtorus.

I don't know why a Galois orbit of a $k_{s}$-torus has only finite tori, can anybody explain this for me? Thanks a lot.

I have some trouble while reading a proof of a lemma in the book

Conrad, Brian; Gabber, Ofer; Prasad, Gopal, Pseudo-reductive groups., New Mathematical Monographs 26. Cambridge: Cambridge University Press (ISBN 978-1-107-08723-1/hbk; 978-1-316-09243-9/ebook). xxiv, 665 p. (2015). ZBL1314.20037.

Here is the lemma:

Lemma C.4.4. Let $G$ be a group scheme locally of finite type over a field $k$, $T$ is a maximal $k$-torus in $G$ and $K/k$ an extension field. If $G$ is smooth or commutative, or if $K/k$ is a separable extension, then $T_{K}$ is a maximal $K$-torus in $G_{K}$.

In the proof, the authors wrote:

Suppose $G$ is connected and commutative. Any $k_{s}$-torus in $G_{k_{s}}$ has a $\text{Gal}(k_{s}/k)$-orbit consisting of finitely many $k_{s}$-tori, so by commutativity the collectively generate a $\text{Gal}(k_{s}/k)$-stable $k_{s}$-subtorus.

I don't know why a Galois orbit of a $k_{s}$-torus has only finite tori, can anybody explain this for me? Thanks a lot.