Someone registered my brand and now Im getting performance notifications?

You would’ve been rejected (regardless of Hilfiger) because it already existed.

https://trademarks.ipo.gov.uk/ipo-tmcase/page/Results/1/UK00003453532

The brand ‘Holteez’ was already registered in December 2019 (active from March 2020), unless the details in that link are yours, you’ve actually been infringing that Trademark since 2020.
You would have to contest the registration with the IPO, and prove that you were already using the ‘Brand Name’ before the current owner of it. But since this was years ago, you might have difficulty proving that you have any rights to it.

Or… The brand owner has recently decided to start selling on Amazon, has now applied for Brand Registry and the bots are now picking up on the fact that you don’t own the rights to it.

It’s not your ‘seller-name’ they insert at the beginning of the title, it’s the ‘Brand’ that you’ve stated they are in the listing.

Unfortunately, you might not have an easy way out of this, as unless you can convince the IPO, you won’t have any right to use the branding, and Amazon are unlikely to accept any changes to the listings unless they come from the owner of the brand.