Hello,
Thank you for contacting Rank Math, and sorry for any inconvenience caused.
It seems that you already created a ticket with a similar issue. Can you please confirm if they are generating the same 5xx erorr?
If not, please share a screenshot of Raw Response from the Indexing API upon submitting a URL.

Click on Send to API and then click on the Show Raw Response button.
We 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.