Thanks Helpme for your comments.
I agree that there were signs of my WW as well, which I should not have ignored, Not that they were big ones, but I am sure that would have helped. I misread my wife for a lot of things she could do.

Anyways, today I got a message from WW that she is panning to buy x,y and z for D's birthday and she didn't know what i was buying for her, so she wanted to let me know.

I see this message as information message, thus I did not reply, though I was thinking that I could have replied "Thanks. I haven't decided yet".
What would be the best approach in this scenario. No message or what I typed above?

I have gone dark and detached to a good extent, but I am still not able to differentiate if I am being cold or being dark and detached.
Her complaints have been that i have been controlling, dominating and emotionally unavailable and thus she has lost self confidence and self esteem (though this comes a lot from her childhood ( I am to blame as well and would not shy away from responsibility). I didn't realize she was carrying such heavy emotional baggage from childhood. So everything I said magnified for her and for me these were regular things/fights that happened between husband and wife).

So my doing 180 would maybe look like being responsive to her thoughts and not ignoring her or being cold.But when I don't reply to messages or reply in one or two words, it feels like I am being cold.(though honestly, nowadays, I don't even feel like replying). So, I am still confused what would be best approach in my case in terms of going dark and detaching vs being cold.

I have another question (Just a thought that came to my mind):

As we say that with time we LBHs get used to being alone and by working on ourselves, we are able to live the new life and start enjoying that.
Isn't it the same for WW as well. She is also having this freedom now, free to be with OM anytime she wants, freedom to make choices that benefit her, freedom from the pain they believe we LBHs have given them (specially after separation)?
Don't they get used to this new life and think this is good life and there is no need to be back to the MR? or is it different for WWs.