Installation

How to actually play music from Spotify?
Why does it fail with Unable to open item for playback (Object not found) when I pass album or playlist via URI?
Why I can’t play and/or see some tracks?
Why I can’t control playback from Spotify website?
Why I can’t set foobar2000 as output device from Spotify website?
Why two separate authentications are required?

How to actually play music from Spotify?

Pass the music URL to foobar2000 via main menu File>Add location... (CTRL+U by default).
URL can be accessed from any track/album/playlist in Spotify by clicking on ...>Copy Song Link/Copy Album Link/Copy Playlist Link.

Why does it fail with `Unable to open item for playback (Object not found)` when I pass album or playlist via URI?

A foobar2000 limitation: it’s not possible (or rather REALLY hard) to use an arbitrary string to load multiple tracks.
It works for the track, because, well, it’s a single track =)

Why I can’t play and/or see some tracks?

Spotify interface limitation: podcasts and radios are not supported.

Why I can’t control playback from Spotify website?

Why I can’t set foobar2000 as output device from Spotify website?

Spotify interface limitation: these features are part of the Spotify Connect interface, which is not publicly accessible.

Why two separate authentications are required?

The component uses two separate interfaces for Spotify integration:

LibSpotify for music playback.
WebAPI for everything else.

Each one uses a separate authentication scheme.