I've been experiencing the exact same problem as in this thread for a while now. I finally decided to look into trying to fix it, but the solution in the linked thread hasn't fixed anything for me. When using the web version of Spotify, Connect does work. I tried reinstalling the iOS app twice, and checked all app permissions multiple times, so I don't think my phone is the problem.
I tried changing windows' proxy settings, which didn't fix anything either. Using a combination of windows and spotify integrated proxy had no results. And of course, I've tried uninstalling and reinstalling the spotify app and installing the microsoft store version (+ multiple 'clean' installs of both).
Thanks for reaching out about this here in the Community.
Just to make sure, are you not able to see the available devices when clicking on the Connect icon?
Also, is this happening across devices or only on the web player?
On another note, could you let us know if the same happens while using a different internet connection?
Lastly, sending us some screenshots of what you're seeing on your end would come in handy. You can attach them to your next response by using the Insert image option in the post editor. Make sure not to send any private info.
Keep us posted.
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“Music acts like a magic key, to which the most tightly closed heart opens.”– Maria von Trapp