How I start Spotify on any Alexa with Home Assistant

At home, my music comes from Spotify Premium, and most of my playback devices are Amazon Alexa devices.
I wanted my daughter to start her favorite songs without handling a phone or a screen. Tap an NFC card on the reader and the music starts: a kind of Toniebox, just built myself. The reader is a DIY build based on an ESP32 microcontroller and ESPHome Builder, following the adonno/tagreader template.
The obvious Home Assistant approach is the official Spotify integration plus media_player.play_media. That is not enough for a cold start, though. The integration can use play_media sensibly only when something is already playing. Starting a specific song, playlist or podcast from a stopped player is therefore not supported by this path. This is a limitation of the integration and its current media_player behavior, not a configuration mistake.
The solution is a small Python script. It asks the Spotify Web API for available Spotify […]