So it seems like she's at least open to working out but maybe just needs a nudge and coach/motivator.There was about a month before the pandemic where we were going to the gym together and planned on running a 5k and she actually started to look better. We also we're having fun supporting each other. But when everything got shut down it went to sht.
I want to find something we can do at home that we both enjoy. When I brought up going in a low carb diet for myself to cut my body fat, she said "you can do it, but that doesn't mean I'm going to do it."
One thing you can try and it is fun and burns off calories is "Just Dance" It's a game for Playstation where you have to try to follow and mimic dance moves. I don't know of any girls that don't like this.
As for diet, I found just cutting out soda, processed foods and eating more natural items(less takeout, more home cooked meals) to help quite a bit. Your diet maybe too extreme for her to start with. Maybe suggest less extreme things like I mentioned.
If both of you are WFH or working at desks all day, get in the habit of walking 1-2 miles a day with her. Try walking in new and undiscovered areas to keep it exciting. Trails, different neighborhoods, different business districts, etc.
Women are always great at subtlety and giving hints that we men often aren't able to process with our thick skulls sometimes. It would then make sense to introduce subtle hints back at women:
Push/Pull, Dropping subliminal hints, Easing into things, Starting off slow and slowly conditioning her behaviour without her really knowing what's going on, subtle training/discipline, etc.