Context
I had this very good friend who told me a few days ago to stop any form of communication that is not work-related. Talking about the situation is not an option as she made it clear that she wants to cut ties completely. Even if I've been hurt by the rejection, I owe a lot to this person as her friendship significantly improved things for me while it lasted. I don't have any grudge against her and I don't think she's mad at me, she is just fed up with me. I think I relied too much on her for moral support.
About the friendship
Over the lasts months we spent several evenings talking, watching series and playing video games, at both our places. We also had a birthday party, had some activities and a lot of fun. We met because we had a common friend we both like a lot and because we both love video games. I've only called her once (and she didn't answer). We used to communicate a lot over emails and direct messages but I drastically reduced my output when she asked me to. I have some friends I communicate with far more often than with her and I never demanded anything from her or insisted when she didn't want to talk. And to clarify, I'm a male and no romance is involved.
Problem
I'm currently working next to this person and while I respect her choice, it makes me feel terribly uneasy to have to avoid all non-work related discussions that may happen in the workplace. And it's even worse for lunchtime or hanging out with colleagues as I don't want to be cut out of the team by always avoiding being at the same events at the same time. I'm doing my best but it makes my days incredibly more stressful than they should. Quitting is not an option and I have to stay with my other colleagues.
Question
My goal is to find a way out of this situation. I could talk to her but it's out of question because it would be disrespecting her will. I could talk to my manager but it would disclose the situation and I know it would be even more awkward for both of us. How can I approach this situation to make it easier for both of us?
Update/"Solved" somehow
I found out I was suffering from depression at that time. With some help I finally got out of it an even if I'm still very sad of losing such a great friend, I don't feel the same pain as before. If you never had to fight depression, like me before the events I had to endure this year, it can be pretty hard to spot what is wrong with you or why everything feels wrong or even why you can't think clearly. Get help, don't wait to lose your friends as you'll be keeping going more and more to them for moral support to the point of tiring them out. Get actual help, don't make my mistake.