Just to confirm, could you head over to the app's settings and make sure that the option to "Publish my activity on Spotify" is toggled on? It should look like this:
If after restarting the app once you've toggled on this setting, you're still having troubles, we'd recommend checking with a different Spotify account (if possible) to see if the issue persists.
Further, we'd suggest asking your friends to make sure that they're following your Spotify account in order to view your activity. It's also a good idea asking them to unfollow you, then follow you once more to shake things up.
Keep in mind that if your Spotify account was created with Facebook, you'll also need to make sure all necessary options are enabled. You can find out how to check this by following the steps in this Spotify Answer.
Let us know how you get on. We'll be right here if you need more help :)
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