Large-parameter conjecture for the normalized generalized summatory function

For real $a>0$, define

$$W_a(x)=\sum_{n\leq x}(-a)^{\Omega(n)}.$$

Let $\widetilde{W}_a(x)$ and $s_a$ be the normalized function and its limit superior defined in the source's preceding theorem. Large-parameter conjecture.

$$\lim_{a\to\infty}s_a=1.$$

Computations suggest that the local maxima of the normalized function approach $1$ as $a$ grows. The conjecture remains open.