Even when you sign up for Instagram using your Facebook account, the accounts are not automatically linked. You need to manually connect your Instagram account to your Facebook page.
Please refer to this Support Article on the Meta Business Help Center website (applicable for web browser and mobile app user).
The following is using a Web Browser:
1. Log into your Facebook account using your web browser
2. Click your Profile icon (top right)
3. Click 'Settings & Privacy'
4. Click 'Settings'
5. In the 'Permissions' section -> click 'Linked accounts'
6. Click 'View'
7. Click 'Connect' next to your selected Instagram account
