Dear Madis Sügis,
Greetings! Thank you for posting in Microsoft Community. We are happy to help you.
Per your description, OneDrive verification code sending takes too long that the verification session expires before you get the code.
For the situation you encountered, we deeply understand the inconvenience caused and apologize for it.
Currently there is a service incident OD544564 which title is Intermittent delays or problems loading OneDrive for Business content.
User impact: Users may experience intermittent delays or navigation errors when accessing OneDrive for Business content.
Current Status: We're reviewing service monitoring telemetry to isolate the root cause and determine our next troubleshooting steps.
Scope of impact: Impact is specific to users who are served through the affected infrastructure.
We recommend you let the file owner who shared with you OneDrive files to contact his Microsoft 365 administrator, go to Service Health Dashboard in Microsoft 365 Admin Center, check whether his tenant is affected by this service incident. If yes, we're afraid the issue you encountered may be related to this service incident. You can let file owner monitor the incident.
If his tenant is not affected by this service incident, feel free to post back end let us know, we will continue trying best to assist you further.
Thanks for your time and understanding! We hope you have a nice day, stay safe and healthy always.
Sincerely,
Tina | Microsoft Community Moderator