If the group is added through LDAP participant profile, the group shows on system security -> participant tab, then you can add the group to access rights and participant users belong to this group would inherit the access rights.
But if the group is added through LF Server, the group shows on system security -> named user tab, then named user users belong to this group would inherit the access rights while participant users could not.
And once you added the group in LF Server, it won't be synchronized as participant group.
See https://answers.laserfiche.com/questions/57266/Forms-Participants-licenses-are-not-using-AD-groups-for-Form-security-access
So in your case, why not add another group in the AD? Keep one group as named group while the other as participant group, and add both to Access Rights page.