Just my opinion, you can take it or leave it. And if my advice offends you, or feels manipulative, just let me know and I will refrain from posting on your thread.
If you decide to hang out, have dinners, while she goes back to her rental, you are in essence easing her transition into singlehood. I think you are doing yourself a disservice by playing along.
She wanted space, right? Then the most loving thing you can do is respect her wish and give it to her. She is testing out what it's like to not be in a relationship with you (and she may be involved with another man), so.... show her what it's like. Remove yourself, respectfully, from her life. Allow her to wonder about, and miss you.
And while she's seeing what it's like without you, make yourself as attractive as possible. Focus on your issues in therapy, build your body, push yourself outside your comfort zone, explore new things etc. And this can make you extremely attractive to your WAS, or to other women (No, I'm not advocating dating), when and if the time comes for you to get back out there.
You can scour the internet, YouTube etc for advice on how to get your W back and you will see most of the advice is pretty consistent. You have to let her go, in order to get her back. The problem is that letting her go will be the hardest thing you have ever done and it will go against every instinct you have to preserve your marriage. Many people can't do it.
