According to Google AI there is a free service but I can't play anything
View attachment 34039
Right, I should have been more precise, I have Amazon Music Prime.
Also, depending on where you live, this feature might not be available. (Just a guess.)
Even if it's just a guess, it's possible. At least the available subscriptions
do differ from country to country for sure.
This is one of my go to links for queries about the differences between Amazon Music subscriptions:
https://www.amazon.co.uk/gp/help/customer/display.html?nodeId=GW3PHAUCZM8L7W9L
E.g., there's no "Standard" subscription available in Germany.
I have something at the back of my mind that says that the Amazon Music API used by WiiM doesn’t support the free service perhaps around its use of ads.
Deliberate (!) limitations of Amazon's API look like the most likely reason to me.
The OP clearly stated that he's on the "Unlimited" plan, so the mystery remains why I do see the buttons (not just on stations) with my lowly "Prime" subscription. My guess is that playlists are not technically treated as playlists on a Prime subscription, at least through their API.
I haven't purchased any songs so far. Or have I?

API integration has mixed feelings about it.
When I try to play one of those purchased, but not purchased songs through the WiiM Home App, the thumbs up/down buttons are gone, indeed:
I created a playlist
only containing the two visible purchased songs, but the API integration in the WiiM Home App won't even let me play those. Instead, a random collection of songs is played.
For me, Amazon Music remains the worst music service in the world.

I left out all the things I had to do to just create these two screenshots in English (including having to change my Amazon profile to US to be able to access an non-helpfull help page that's not available in any other region

).