Everything is enabled/allowed.

And that doesn’t explain why listening music on any of my desktop apps don’t affect the shortcut suggestions. Maybe that's because Recently Played music doesn't sync to the web player as well? So if web player doesn't see any listening history then it doesn't offer anything new in the shortcuts as well?
I did a video for you. Explanation to the video:
1. I start playing Your Time Capsule in my Mac's desktop app.
2. Then I open the web player where it shows Your Time Capsule in the Recently Played section
3. Then I switch back to the desktop app and close it
4. Then I switch back to the web player and refresh the page
5. And the Your Time Capsule is gone from the Recently Played section in the web player
Notice the other playlists in the Recently Played section. I listened to them in the web player and they synced to the desktop and mobile apps just fine.
So yeah, it seems to be that something is broken with history sync between platforms and that also affects the shortcut suggestions.
Hey folks,
Thank you for reporting this issue to us and all your info.
We just wanted to let you know that the right folks are looking into this.
We're not able to provide an exact timeline for a fix, but we'd recommend always keeping your Spotify app up to date to ensure you're on the latest version.
Thanks for your understanding!