It can be very case-by-case. Some badges are tied to the person, not the profile, so they do move. Others are tied to the profile’s participation here on the site, and don’t move.
In your case, your Magical Inkwell would transfer to a new profile (or be added to an alt profile if you wished) because that is tied to your personal work.
But all the others are tied to events. Any new profile would not have participated in those events, so giving them to a new profile would absolutely cause confusion for people who felt they should have gotten the same badge but did not.
Also, your upload total does, in fact, properly reflect the number of images you uploaded. That number is not the number of images you want to be publicly associated with, it’s your total uploads - including deleted and anonymous uploads.
I want to start on a fresh account
Just send me a PM with the word “Yes” and I will do that thing I have been offering to do for 3 months. Then you can re-use your current email on a new profile, which appears to be another thing preventing you from being able to create the kind of presence here that you want.