Hello @yan simkin
Is there a chance that this online account (I assume we are talking about a "live" account, such as outlook or hotmail) has not been configured at some point as "Work" or has been associated with a Enterprise or Business contact. In that case, this accounts will not work in the same way for recovery, and local administrator will be required.
Another solution would be to Repair Windows, but choosing the options "Keep My Files" during the repair operation.
There are other valuable advices in the next thread, with different workarounds that you may want to try: https://answers.microsoft.com/en-us/windows/forum/all/automatic-repair-wont-let-me-log-in/afb887ca-c14e-45c4-92f5-ea14729e5f6d
Hope this helps with your query,
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