In order for multiple family members to have access to Medium membership on their accounts, each of these accounts will need to have a separate membership subscription.
What the App Store badge “Supports Family Sharing” means
Though the App Store listing for the Medium app displays a Supports Family Sharing badge, this message should not be understood as a guarantee that a single Medium membership subscription can be shared by up to six family members.
The badge is by default displayed for iOS apps which can be downloaded and used by multiple family members enrolled in the Family Sharing plan. And accordingly, its description says:
With Family Sharing set up, up to six family members can use this app.
In-app purchases such as Medium membership are not covered by Family Sharing
While our iOS app is indeed completely free to download and use, a Medium membership subscription (which gives readers access to exclusive content and features) is an optional in-app purchase, and as such is not eligible for Apple Family Sharing.
You can learn more about what types of purchases cannot be shared by family members in this Apple Support article.