I sent my almost 3 year old OPN 1 hearing aids in for a check last month as the warranty was up near the end of the month. They came back with new serial numbers and the Oticon ON app showed Software of 6.0 and firmware as au2cs3fw5.16.0. My provider updated the firmware (now shows Software of 6.1 and firmware of au2cs3fw5.16.1) before putting back in the custom configuration that we had worked out for wind noise reduction and so on.
I have not had the shutdown/reboot issue for quite some time after updating the OPN firmware to 5 (if I remember correctly), the TV adapter firmware, the ConnectClip firmware, IOS on my iPhone 6+ and the ON app (1.something). There are too many possible issues and interactions so you may need to update more than just the hearing aid firmware. That said, Oticon may very well need to further update the HA firmware to work with 13.x.
I did have some strange interactions like volume shifts (no turning off/rebooting however) when I had my new OPN S 1 aids paired with both an iPhone 6+ (IOS 12.4.1) and an iPad Pro (iPadOS 13.1.2) both with the 2.0 ON app. Those problems seem to have gone away after I deleted the pairing in the iPad Pro (I use the iPhone much more than the iPad).