Based on some of the network analysis I did on my phone, I think this is related to Facebook's analytics engine. Most apps I've seen communicate with graph.facebook.com to send telemetry (when which screen was opened etc.).
It wouldn't be beyond Facebook to immediately connect that telemetry to your user profile, making these apps show up in your profile.
Why would Google send anything to Facebook from its Home app ( the one used to control Chromecasts )? It's beyond short sighted to feed data to a competitor.
They have the same customers and customers have a finite advertising budgets. When Facebook gets more Google data it benefits the "result" of the ads on facebook which in turn over time gets more $$ shifted there.
1. Who knows what data Google is giving back in return?
2. Neither want a monopoly. A duopoly is far more resistant to regulation.
3. Many business will advertise on multiple channels. So long as they edge out the others it's fine by them. They know they are the two premium outlets.
Root your phone and use a community made ROM? Vendor bloatware that comes with your phone is and always has been garbage. The only reason phone vendors have to develop and ship apps on their phones is to sell you out, to improve their unit economics.
Google Chromecast shares activity with facebook!