Hello,
We apologize for the issue you are facing with the update. The "PCLZIP_ERR_BAD_FORMAT (-10)" error can occur for a few reasons, even if you have a PRO account and sufficient server space. Here are some steps you can take to resolve this issue:
1. Check the Zip File
Ensure that the plugin zip file you are trying to upload is not corrupted. You can download the latest Rank Math PRO version from your account and try installing it again.
2. Update While Connected to the Correct Account
Make sure you are not trying to update the PRO version while connected to a free account. Confirm the email address associated with your Rank Math account and ensure you are logged into the correct account. You can disconnect and reconnect your account by navigating to Rank Math SEO → Dashboard → Help and clicking on Disconnect Account.

After disconnecting, click on Connect Now to reconnect your account.

3. Server Configuration
If the error persists, it might be worth checking your server configuration or contacting your hosting provider to ensure there are no restrictions or issues that could be causing this error.
If you continue to experience difficulties, please reply to this ticket, and a human agent from our support team will assist you further. Thank you for raising this concern, and we appreciate your patience as we work to resolve it.
Sources:
How to Fix PCLZIP_ERR_BAD_FORMAT (-10): Unable to find End of Central Dir Record signature » Rank Math
Hello,
Thank you for your query and we are so sorry about the trouble this must have caused.
Assuming that the Free and PRO versions are already installed on your website, please reconnect the website with the correct account to fully utilize all the features.
Please reconnect the website to your Rank Math account and then clear the Rank Math Transients by going to Rank Math > Status & Tools > Database Tools > Remove Transients:

If the issue persists, we might need to take a closer look at the settings. Please edit the first post on this ticket and include your WordPress & FTP logins in the designated Sensitive Data section.
Please do take a complete backup of your website before sharing the information with us.

It is completely secure and only our support staff has access to that section. If you want, you can use the below plugin to generate a temporary login URL to your website and share that with us instead:
https://wordpress.org/plugins/temporary-login-without-password/
You can use the above plugin in conjunction with the WP Security Audit Log to monitor what changes our staff might make on your website (if any):
https://wordpress.org/plugins/wp-security-audit-log/
We really look forward to helping you.
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.