The picture of your Manychat account is sourced directly from the connected Facebook page. If your Manychat account displays a question mark instead of the avatar, this indicates that age or country restrictions have been set up for the connected Facebook page.
If these restrictions are unnecessary and you want your profile picture to display properly in Manychat, you can remove the restrictions by navigating to Settings > Audience and visibility > Followers and public content:
Please note that the question mark replacing the profile picture is visible only inside your Manychat account. It has no effect on your Facebook page or the experience of your users, so you may choose to leave the restrictions unchanged.