Please refer to your appointment letter for the standard guidelines mentioned for separation from the firm. What does it say about your notice period? Did you discuss your notice period with your prospective employer during the interview?
The submission of resignation begins the process for separation from an employer. Your manager has processed it but has not accepted it.
The HR team has mentioned a condition: Knowledge Transfer is vital. However, is the back-fill mentioned as a condition for separation in your Appointment Letter?
Please work alongside your reporting manager to create the document for Knowledge Transfer in case there are no team members to be trained by you.
If you don't have the time to serve the notice period, offer the HR to buy it out.
Write a detailed letter to your manager, marking a copy to your HR, mentioning the time duration you would be able to serve your firm. Provide an end date beyond which you wouldn't be available. Offer to buy out the remaining duration of the notice period, if any. Offer to settle all dues and complete the transfer of responsibility and knowledge. Share the complete timeline. Finally, mention that if no response is received within 3 working days, it will be considered as an acceptance of the resignation.
If possible, send this as a registered letter. In case you have to email this, keep a hard copy of the receipt from your inbox.
Talk to your new employer about the release and keep them informed about the developments. Seek to understand the Experience Letter and other documents that they would need to validate your release.
Above all, remain very supportive of your reporting manager. Request a letter of recommendation from him. Hand over all company property, such as a laptop, cell phone, hard drive, and other company-owned items that you have, to your manager. Take it in writing that you have handed them over to him.
Wishing you all the best!