@futurebird@kechpaja here in Germany, any "no pets" roles, and any rules that tenants must get a permission for a pet from a landlord, only apply to "uncontained" pets; "contained" small pets (those that do not interact with the rental property directly) are explicitly excluded by law.
So having even a thousand of hamsters does not violate any "no pets" rules as long as they're in their cages / aquariums and are not free roaming all over the apartment.