It’s better if you at least ask them for a password to check your email. This way you will actually make sure that the email address belongs to the user.
If you automatically log in, you just make sure that the email address exists and that the user who owns this email address wants to access the account.
Regarding the third point: you hope that you trust only the person (s) with access to this address, as soon as you confirm that the address really belongs to the user (which you could do by requesting a password during verification).
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