The page is connected to ManyChat, but the "Get Started" button does not appear in Messenger.
To clarify: "Get Started" button is a mandatory Facebook feature which you can see in the Messenger chat box before starting a conversation with the page - users have to press it in order to start receiving messages from the Bot.
If a page was connected by a user with the 'Editor' Page Role for this Fan Page on Facebook, it may result in the absence of the "Get Started" button.
Here's a solution for this case:
Please note this must be done by ManyChat Admins with the 'Admin' Page Role on Facebook for this page: while in your ManyChat account, head to Settings => General and hit 'Refresh Permissions' button. If this doesn't help, try to re-publish Main Menu or Welcome Message on this page - "Get Started" button will appear on Facebook then.
Hopefully, this helps!