Can I leave after serving 2 months notice period, since I didn't acknowledge the updated notice period

I am currently serving my notice period of 3 months. In the offer letter which was signed by me and the employer, it states that the notice period will be 2 months. However, recently, before my resignation, they updated their notice period to 3 months and sent an email to all the employees informing about this, but they did not ask for any acknowledgment in that email.

Can I leave after serving 2 months since I have not acknowledged the updated notice period, and the one that is mentioned on the offer letter is 2 months?

I have served half of the notice period and also tried to buy out my notice period, but my employer declined my request to buy out. Is it right for the employee to leave the organization by paying for the days they are not serving notice for, or is it under the employer's authority to allow or deny the buyout of the notice period? Can the employer deny issuing a relieving letter and experience letter even after paying the salary for the days not served?

Below are some points from the employee manual. Are any of these points not in accordance with the rights of an employee during the notice period?

- In case the proper notice period is not served as per the policies, the employee will be liable to pay back the salary for the number of days not served.
- Relieving letter and experience letter will be issued to only those employees who follow the policy and serve the proper notice period.