Taste profile is indeed rolling out in the US and that will help you steer Spotify towards more discovery (or whatever you want) in general (specifically your home/start page). Discover Weekly is however (still/for now) its own system so that will take a bit longer (but the vision is full control over all playlists, including DW).
What you can do in the mean time is to essentially create your own Discover Weekly with the traits you specifically want using our Prompted Playlists feature.
You can essentially write your own ”algo” using both world information (I.e. ask it to read/check the internet, web sites, charts, events, concerts, social media etc) as well as your personal information (your taste, genres, favorite artists and your detailed listening history all the way back to 2008). So you can ask it to avoid covers, avoid genres you’re bored with, only ever recommend tracks you’ve never played before etc. It’s pretty powerful.
You can also schedule it to update daily or weekly.
Hope that helps as we keep building out more control!