There's no code to send the confirmation email multiple times. If you delete the account and re-create it with same email address then yes you will have to confirm it again. I'm seeing no such issues in my tests.

Ensure Joomlas email is not sending by editing "User - Joomla!" within Extensions > Plugins and setting "Notification Mail to User" to "No". Next ensure Joomla isn't sending confirmation emails about Joomla accounts by setting "New User Account Activation" to "None" or "Self" and "Send Mail to Administrators" to "No" in Users > Manage > Options.

If still having issues begin unpublishing non-core CB plugins 1 by 1 within CB > Plugin Management. If issue persists repeat for 3rd party Joomla User and System plugins in Extensions > Plugins. It's possible something is causing multiple user stores to trigger resulting in the email being sent multiple times.

I don't know what to suggest. There's no core code to send multiple confirmation emails unless something is trigger user store over and over to result in that behavior. If using CB Auto Actions try unpublishing it as it's possible one of your auto actions could be doing it. You're also using AcyMailing which could be causing this if you're using their Joomla user block. You need to disable 3rd party extensions and plugins entirely 1 by 1 to find the possible culprit.

Is that captcha provided by CB AntiSpam or Joomla plugin? If from CB AntiSpam I can't see how as registration would be blocked before any email could be sent. If Joomlas then it's possible it's not properly erroring the user object and causing some sort of loop.