Since the recent update to the Instagram app, a pop-up window on a song title page will automatically offer to add the song to your Spotify playlist. The prerequisite is that you link the two accounts together. You will receive the request when you navigate to the page of a compatible song for the first time since the update. Either via a story or post or by entering a song title directly in the search and navigating to the “Audio” tab.
If you agree to the link, you allow Instagram to access some aspects of your Spotify account. Linking allows Instagram to see your Spotify account information, including your (user) name, profile picture, followers and public playlists.
Instagram also has access to your activity on Spotify, such as recently played content, the content you have played, the content saved in your library, and your personalized playlists. Additionally, Instagram may take actions on Spotify on your behalf, such as adding or removing content from your library.
Although the permissions sound very restrictive at first, they should generally only be used to add the songs listed in Instagram to your Spotify playlist if you wish. How exactly Meta, the company behind Instagram, Facebook and WhatsApp, handles the account data obtained is not clear from the linking conditions.