Problem: my connected devices only appear in my desktop client when I connect to them from my phone client.
I have a Google Home in my home office. When I open my laptop, that device does not appear in my Spotify Connect list. I then go to my Android phone and start Spotify. From there, I connect to the Google Speaker.
My laptop Spotify client instantly recognises the Google Speaker and it's added to the list.
Everything is on the same wifi network, connected with no problems.