Hello, I’m sorry to hear about the issue your worker is facing with updating pages using Rank Math. It seems like all the necessary options are checked in the Role Manager, except for Role Manager and Top Bar. This should allow the author role to make changes using Rank Math.
If the issue persists, I recommend checking if the user capabilities for the Author role have been granted correctly in the Role Manager settings. After enabling the required user capabilities, please ensure to click the Update Capabilities button at the bottom of the page to reflect the changes.
If the issue still persists after these steps, please let us know, and we’ll be happy to assist further.

Thank you for bringing this to our attention!
Sources:
How to Use the Role Manager Feature of Rank Math SEO Plugin
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This is an automated reply from Rank Math Support Bot. If you need further assistance, please reply to this topic and a human support agent will reply to you shortly.
Hello,
Since we did not hear back from you for 15 days, we are assuming that you found the solution. We are closing this support ticket.
If you still need assistance or any other help, please feel free to open a new support ticket, and we will be more than happy to assist.
Thank you.