Feedback sent through Microsoft Edge Chromium is completely separate to feedback sent through the Feedback Hub.
If you want feedback history, you have to add your email to the email field. To see it, go to your inbox and any feedback you have sent with your email will be there. The feedback tool remembers which email it was if there even is one. By default, it doesn't fill in your email in incognito windows which is good. This lets you send it anonymously or lets you clear the URL and add your email (or whatever you want :p)
Now I realise that it's a bad idea that they changed the feedback icon. Microsoft also has Uservoice, the Feedback Hub, GitHub and various feedback tools like Office. but... It makes sense. Edge Chromium is available on platforms other than Windows 10 and the Feedback Hub is a (really bad lol) UWP app. So I guess GitHub is for open source stuff, Feedback Hub is for UWP stuff, some Office products and Mixer have Uservoices and the rest have other stuff. If you're wondering, the feedback tool in Edge Chromium is the from Chromium/Chrome's. They've just changed and added stuff