Hello,
We apologize for the inconvenience you’re experiencing with connecting your Google Search Console and Analytics to Rank Math. It seems like there might be an issue with the connection settings.
To resolve this, we recommend testing the connection to your Google account. To do this, please navigate to Rank Math SEO → General Settings → Analytics and click on the Test Connections option at the top right of the Analytics settings.
Here’s a screenshot to help you locate the Test Connections option:

After clicking on the Test Connections option, Rank Math will validate the existing connections. A green signal indicates a valid connection, while a red signal indicates a glitch in the corresponding connection.
If you see a red signal or encounter any issues during the test, you can try reconnecting your Google account by following the steps provided in this screenshot:

If the issue persists even after reconnecting your Google account, or if you see a red signal again when you validate your connection, please share the error log with us by opening a support ticket here.
We hope this helps resolve the issue. If you need further assistance, please feel free to reach out.
Kind regards
Sources:
How to Verify Your Website on Google » Rank Math
How to Connect Your Google Account With Rank Math SEO » Rank Math
Resolving Rank Math Analytics Related Issues » Rank Math
Rank Math General Settings
Hello,
Thank you for contacting Rank Math support.
We have already replied to your other ticket with the same concern, and please continue there to avoid duplication.
I’ll close this one so we can follow up on one thread for efficiency.
Looking forward to helping you.
Thank you.