I realised what the problem was in my case: I recently turned on 2-step verification for my outlook.com ("Hotmail") account, which means that the password I log in to the website with will not work for a third-party (i.e., Calibre).
If anyone else has this problem and they've turned on 2-step verification for outlook.com, look in outlook.com's Account Settings > Security, and you'll find how to get a one-off, application-specific password which you can then use instead of your normal account password.
In summar: my fault, not Calibre's.
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