Recently, Hotmail 📧 has started to offer its users the new design, part by part. However, this design also brought with it a problem with Opera. Although it has been stated that the problems such as not being able to click, view messages, open folders in Hotmail will be fixed by Opera as soon as possible, let's share the quick solution.

To Troubleshoot
To fix the problem, you need to update the Browser Script. You can find detailed information here, but let's briefly explain it here.

Go to the browser JavaScript setting and replace it with the valued 1 there.
Save the setting with the "Save" button at the bottom.
From O Menu > Help > Check for update.
Opera will update the Browser Script in the background even though it says there is no new version. When you check Hotmail again in a few minutes, you will see that the problem is fixed.