Question about Hilbert transform of a cosine signal
Make sure that you understand the conditions under which

$$\mathcal{H}\big\{A(t)\cos(\omega_0 t)\big\}=A(t)\mathcal{H}\big\{\cos(\omega_0 t)\big\}=A(t)\sin(\omega_0t)\tag{1}$$

holds. Eq. $(1)$ holds if $A(t)$ is a low-pass signal with a cut-off frequency smaller than $\omega_0$. This implies that $A(t)\cos(\omega_0t)$ is a band-pass signal with no energy at DC. Eq. $(1)$ is a special case of Bedrosian's theorem.

In your example, $A(t)$ is not band-limited, and, consequently, $(1)$ doesn't hold. However, if you increase the modulation frequency $\omega_0$, the overlap of the spectra of $A(t)$ and of the carrier becomes smaller, because $A(t)$ does have a low pass character. So for large $\omega_0$, Eq. $(1)$ is approximately satisfied, which is exactly what you see in your plots.

Also take a look at this related answer.