Ever since I knew about anxiety five months ago, I started going easy with life, started to distract myself from all the stressors. I used to be very alert before deadlines previously and hence it used to interfere with my life severely. Now that I try to relax and use stress handling techniques, I feel better but I am missing deadlines. Today I got the rejection letter for a paper I submitted, which I know happened because of going easy on the deadline. Now what should I do to balance both sides?
The first, and most important, step should be to find a good therapist to work with you on your anxiety if you don't already have one. If you already have one, talk with them about how you are feeling about this rejection. They will be in a much better position to talk you through your options than we random people on the Internet.
Keep in mind that this isn't an academic question per se (even though it often comes up in academic contexts), and professors and fellow students are not necessarily the best people to help you. Speaking from a little personal experience and seeing the same process in others, getting help with anxiety, burnout, and stress-related symptoms is not about finding a magic bean strategy that will allow you to put in the same hours as before, but somehow don't mind it anymore - it's about guiding you towards acceptance that you cannot and should not work quite as hard as you used to, along with the consequence that you may produce less output than before (but in exchange get a much better life, as you yourself said).