The 7 email notifications today were a fair warning ...

This is going a bit over the top though?

By the way, I assumed this would just auto renew?

But I clicked on Renew Now, and it takes me to my sites. I click on Manage this purchase for the relevant site, but I can't actually see anywhere to renew it?

It will auto renew if you have a valid payment method on file. We have a bug report in for that duplication issue. Could you let me know which site this is for?

st*******.com

That license was already renewed on Thurday last week. So you wouldnt see a renew button in your client area. You have already renewed it. If you are still seeing the items in your admin CP you can dismiss those. If you go to System>License key and refresh, it should actually remove them itself anyway