Page is connected to ManyChat, but "Get Started" button does not appear in Messenger. "Get Started" button is a mandatory feature of the Facebook Messenger platform: users have to press it in order to start receiving messages from the Bot. If a page was connected by Editor, 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 Admins: while in your ManyChat account, head to Settings => General and hit 'Refresh Permissions' button. If this doesn't help, try to republish Main Menu or Welcome Message on that page - "Get Started" button will appear on FB then.