According to laws of the newly formed Austrian Republic every Habsburg might become a citizen as well as obtaining residency if only they would officially abandon any claims to govern. Wilhelm chose not to abandon those claims and de jure lived in Vienna illegally.
In accordance with the laws of the newly formed Austrian Republic, Habsburgs were entitled to acquire citizenship and residency, provided they surrendered their claim to rule. Wilhelm chose not to surrender his claim and therefore lived in Vienna without proper authorization.