The infinitude conjecture for Galois number fields with trivial relative class group

For a number field $K$ Galois over $\mathbb{Q}$, define the relative class group

$$\widetilde{Cl(K)}:=Cl(K)/Po(K).$$

Here $Cl(K)$ is the ideal class group and $Po(K)$ is the Pólya group of $K$. Infinitude conjecture. There exist infinitely many number fields $K$, Galois over $\mathbb{Q}$, such that

$$\widetilde{Cl(K)}=\{0\}.$$

The claim asks whether infinitely many Galois number fields have class group equal to their Pólya group. The source does not provide a proof or indicate that this conjecture has been resolved.