After a thorough investigation, I have successfully been able to fix the issue. The issue was happening due to some HTML Meta data that was somehow added with each heading and paragraph content on that page. Please check this screenshot(hidden link) for a better understanding.
Those data were also getting added with the translation job which was increasing the job file size. As a result, ATE was unable to process the job and an error was thrown.
I deleted those data and now the Translation editor is getting loaded properly. Please check this screenshot(hidden link) for a better understanding.
If you ever encounter this issue in the future, please check the Heading and paragraphs and if you find the same metadata, make sure to delete them. Also, if you're pasting any content, after pasting, also check if any Meta data are pasted with it or not. I hope you can understand.
Please let me know if there is anything else you need help. I will be happy to assist you.