Microsoft has released an updated web version of the Xbox Store. However, it is under a gradual roll-out, so not everyone will instantly see the change. Reportedly, it is fully available to users in Canada. Microsoft didn't officially announce it yet.
Due to this, it remains unknown when the new store design will become available in other countries and regions. But if you want to try out the store now, then just follow this link.
The updated web Store version has got a new design that matches the current Xbox style. Also, you will find several new features. For instance, it now allows you to add games to your wishlist, quickly redeem product codes, remotely install games on your console(s), etc. There is an option to give away games to your friends, and play games from your Xbox Game Pass Ultimate subscription right in the browser. The latter is possible thanks to the Xbox Cloud Gaming (xCloud) project.
Thanks to @tamelucas
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