Yes, you are right that MDR does not state that this should be ISO 13485. However, in Article 8 – Use of harmonized standards is stated that manufacturers must be in compliance with standards that are published in the Official Journal of the European Union. Currently available is the list published 17- 11-2017. On that list is more than 300 standards and the only standard that is covering the quality management system is ISO 13485:2016. That is why it is expected for the manufacturers of medical devices to have implemented ISO 13485:2016.
Of course, since there are a lot of standards on that list that have since been revised, it is expected that a new list of harmonized standards will be published after 26 May 2021, with regard to the full entry into force of the MDR.