Can you be a little more specific and provide more details? Both of your posts don't give much information; instead, they just confuse me more.
Questions About Your Resignation
When did you resign? Did you submit your resignation over email or in hard copy? Did you receive an acknowledgment of the receipt of it?
Counteroffer Discussion
It is very common to discuss and offer counteroffers to retain exiting talent, so how did they approach you? Was there a meeting where they offered you a counteroffer? Were minutes taken, was the meeting recorded, or did they provide anything in writing regarding the same? (I presume no from your first post where you mentioned you had to ask HR to provide in writing about the new offer, which was misunderstood as you wishing to stay).
Notice Period and Communication
Were you on vacation during your notice period? (Usually, leaves are not allowed in the notice period unless there's an emergency - again, as per my knowledge). How was the communication made to you about the cancellation or rejection of your resignation? Over email? When?
Decision Making
What do you wish to do? Are you confused about staying or leaving? If you really didn't have to think twice or were very confident about your new commitment, why did you have to ask HR to email you the counteroffer? If you think you needed some time to think, did you convey the message to HR that although the offer was lucrative, you're not interested and would like to resign?
There is too much lack of information; I can't really help.