I read your post three times and do not understand what you are writing about.
That you do not know what a mailto-link does, tells me, you are not on a regular desktop computer where things are configured. All that button does is open your operating system's designated mail client with the recipient prefilled. So "manually" sending an email to support is exatly what would have happened.
That you can post at all tells me, that you were able to access your account. So, really, I do not understand what your problem is, or why you 1) know you were sent a mail, that you 2) did not recieve and 3) you need for what exactly? To log into your account, from where you are already logged in are posting in public message board?
And I do not understand what you mean with subscribed and Itch being in your inbox, yet you can't find the mail that is in your inbox. What.
Btw, this is community support and not tech support.
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You are probably logged in via cookie and tried to access things in your account that need password entry. And for that, Itch sent you a verification email. That you did not yet receive.
Did you check https://itch.io/user/settings/email-addresses , if your mail adress is correct?
If Itch sends you notifications and stuff like that, it should work. And if you have already contacted support, you should have gotten a response mail with a ticket number.