That functionality already exists, is simple, more granular than a simple ‘Home’ option (which ‘home’ precisely?)

Click on the ‘M’ or the ‘Medium’ icon/graphic at the top left of every page to return to your Medium ‘home’ page.

Click on the publication’s name/icon to return to the publication’s ‘home’ page.

Click on the author’s name/icon to return to their ‘home’/profile page.

Click on your own name/icon to return to your ‘home’/profile.