@Ondřej Želazko, Thanks for posting in Q&A. From your description, it seems an account with domain "email.cz" auto sign in Microsoft 365 admin center. Please chick the account in the right top to sign out this account and sign in with your business account into Microsoft 365 admin center.
Please try the above suggestion. If it is still not working, you can ask in the following Microsoft 365 forum to get help.
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