@Martin Gustafsson Thank you for reaching out to us. As I understand you are using Feitian K9 security key for login to O365, same is not working in Edge/Chrome.
Certain FIDO2 keys have bugs in the firmware/software used by the key itself. Nitrokey and Feitian keys have been known to fail due to bugs in the key. The bugs may not manifest in all FIDO2 capable/supported browsers.
Some of these keys allow firmware updates to resolve bugs, you can review edge/chrome device-log if you suspect the key has a bug.
How to view device logs - chrome://device-log/ or edge://device-log/
Please make sure, where applicable update firmware/software, would request you to check the relevant vendor's support to get details on updated firmware availability or replacement keys.
Let me know if you have any further questions, please feel free to post back.
Please remember to "Accept Answer" if answer helped, so that others in the community facing similar issues can easily find the solution.