Oh I see. Yeah, IMO 4 months is a really long time to be in that situation. Can you stay with a friend? Or family? Or look for a month to month type deal. On Craigslist maybe. It is going to be torture for you. Not to mention this will also be a proactive move (instead of reactive) on your part. It will give you a sense of empowerment. And she will probably see it as such as well. Which wouldn't hurt.

Now, the shitty thing about break ups, even mutual ones is that there is always one person that has moved on sooner than the other. She has moved on. Her words basically translate into that. She is disconnected from you emotionally and is being a bit selfish in not wanting to attempt at being there. She may be avoiding it and supplementing that pain with the other guy. But you cannot control what she does. I know it sucks but that is the truth. All you can do is control how you react and deal with it. Don't let it make you feel worthless. Because you aren't. It seems like it is just her coping mechanism. It might be good that it ended. It is a bit of a red flag that she is jumping right into another relationship instead of taking some time to be alone. She probably wasn't there for you emotionally all that much when things were good. But I don't know your situation so that is purely speculatory.

About the working out, like I said, fuck the gym and put crossfit on hold. You need to center bro. Crossfit is very demanding and taxing on your body and mind. You need simple. Running and walking is simple. And it is very therapeutic for depression and anxiety. If you are competitive by nature, set some loose goals for your runs. Easy goals that will almost guarantee success.