How to Add Spotify to Notion
Two things get tangled in this question. Notion has no official Spotify integration, and Spotify's own embedded player is unreliable inside a Notion frame, so playback frequently fails. What does work every time is cover art in the image widget with the Spotify link on it, which sends people to the app where the music was always going to play properly.
Why the embed misbehaves
Spotify's player has rules about where it is allowed to run. Inside a Notion frame it often loads and then refuses, or gives a short preview, or works on a laptop and quietly dies on a phone. Inconsistent enough that building a page around it is a bad bet, and there is no workaround. Anyone offering one is describing something that happened to work on their machine.
The version that works
Album art or a playlist cover as a PNG in the image widget, with the Spotify link on it. Put a marquee widget above it with the playlist name scrolling and the whole thing reads as a player. Not the same as an embedded player, and it does not break.
If Spotify changes its mind
We will build it. Tag @theplusso on X if you want a nudge when that happens. The general version of this trick is in make your own Notion widget.
The same limits elsewhere
This is not a Notion problem specifically. Spotify's player behaves the same way inside Coda, Craft, xTiles and most Google Sites pages, because the restriction lives on Spotify's end rather than the host's.
WordPress is the exception, since a self hosted site can use Spotify's own oEmbed support and gets a better result. If you keep both a WordPress site and a Notion page, put the real player on the WordPress side and the cover art version in Notion.