Serving Notice period but no KT happening

Is it normal in MNCs to not find a replacement till the end?

Irrelevant. What is normal or not doesn't really matter for your personal situation that you have to deal with. This being said, it certainly happens.

Do they have the authority to extend my notice period even when I serve the complete 3 months of it? ...

No. Your notice period is part of the contract and cannot be unilaterally changed.

If they eventually end up asking/threatening me with a relieving letter delay, considering I don't wish to stay even one more day here, what are my rights? How to respond to such situations without burning bridges?

Unfortunately the legal situation around the relieving letter is murky at best. There is no hard legal requirement for an employer to issue one and they can try to delay or withhold for any or no reason.

You should really consult with a local labor lawyer on how best to proceed. Chances are best shot is here to formally request one in writing starting NOW and keep a paper trail of all your requests and answers if any. Make sure that the request states that you formally request one, that to your knowledge you are meeting all the requirements for getting one and that, if the employer has concerns, they should specify them right now so you can address them timely before your departure. A lawyer can help you write this request.

Knowledge transfer is your manager's responsibility, not yours. They have to be clear about what needs to be transferred to whom.

It also would be good to read all HR policies around this (HR website or employee handbook). If you are lucky there is a written policy about relieving letters. Make sure you meet all of your requirements in there and reference it in your request letter.

I read on this platform that it's better to email your manager and HR regarding knowledge transfer. What exactly should I mail? And I have 2 different HR's: exit HR and the one assigned to me since day 1, but we never connected, so who should be tagged in the mail?

Again a local lawyer can advise you. If in doubt go wide: copy the manager and both HR people.

Good read: https://corridalegal.com/can-an-employer-hold-an-employees-relieving-letter-in-india-know-your-rights/

This was my experience also here. People wait till the last 1week and then hurryup with the KT. The management, in my previous company, generally starts with interviews 3months after the person had left --meaning they go with bad planning. You can go to courts/ lawyers, but stay away from them.

The best you can do

• document the KT on internal confluence
• So when they hurryup with the KT, you have some material in hand to make it easier.
• Talk to finance, get your final payment in email. Verify if its accurate (in my case it was not).
• Taking KT is the companies job. Not yours. Stay calm. Stay professional. And you walkout on the final day, with out regrets (this is what i did).