Cest_Moi, I just read your whole thread and I feel like I could've written so many of your posts myself!! My H has also struggled with depression and we are in what I think he feels is an in house separation, with my H making comments about moving out. We are doing the same dance as you are with my H being cold and hot, sometimes affectionate and other times withdrawing. And my H's love language is also physical and one of his complaints was that we were never on the same wavelength in terms of frequency. I've wrestled too with wondering if I should try to initiate intimacy, but have received guidance that he likely is only using me for satisfaction.
I don't feel like I'm wise enough to dispense advice but just wanted to let you know I'm in the trenches with you. My H also will tell me he's running an errand and be gone for hours (which is awfully strange at the time since I'm in a state where bars, restaurants, etc are shut down...) and I struggle so much not asking what he's doing. In the past, we've always been transparent with each other so it's tough for me. I'm working on feeling more confident about myself and sometimes it means faking it til I make it. I also find that if I come and go to the house and don't tell him everything I'm doing, it piques his curiosity..