OK; I see what’s going on. Whether this behaviour is surprising/could be improved … maybe, but:
[outputs]
home = ["html", "rss", "fb"]
page = ["html"]
Will not render the regular pages as fb, hence when you list them on the home page, there is no fb version to pick, so we choose the default html version.
Changing it to the below will give you the expected output on the home page, but it may not be what you want.
[outputs]
home = ["html", "rss", "fb"]
page = ["html", "fb"]