My question is related to this, this, and this older questions.
Let $\mathcal A_*$ be the dual Steenrod algebra.

At $p=2$, the algebraic group $Spec(\mathcal A_*)$ can be naturally identified with the group of automorphisms of $Spf(\mathbb F_2[[x]])$ (with $x$ in degree $1$) that preserve:
• the group law $x_1,x_2\mapsto x_1+x_2$,
• the tangent space at the identity.

When $p$ is an odd prime, the algebraic super-group $Spec(\mathcal A_*)$ can be naturally identified with the super-group of automorphisms of $Spf(\mathbb F_p[[x,\theta]])$ (with $\theta$ in degree $1$, and $x$ in degree $2$ — this is an exterior algebra on $\theta$ tensor a polynomial algebra on $x$) that preserve:
• the group law $(x_1,\theta_1),(x_2,\theta_2)\mapsto (x_1+x_2+\theta_1\theta_2,\theta_1+\theta_2)$ ????
• the tangent space at the identity. ????

Are these statements correct?
If yes, where can I read about them?
If not, how does one fix them to make them correct?