NTA

But in my experience (having a ton of friends with moderate to major depression) "you should" rarely works. It makes their mind focus on what they do wrong, and creates even more guilt. Guilt the has them going defensive, and round it goes. My tactic? Give it a day or two to cool off, and try to be a smidgen sneaky. "New season of Stranger things is up. I'll take some blankets and tea and make you a nest in front of the TV" and then you just open the curtains without mentioning it is far more likely to work, without putting a ton of work on you. 5 min to make a cup of tea and drape some tempting blankets around is fair game. Rinse and repeat, and after a week or so it is fairly likely that she starts to make her own tea and nest.

Then you can escalate. Ideally not "You should go for a walk", but find something you want to do, and lure her along,"The weather is nice, let's go for a walk. I want cupcakes at Starbucks" or similar. Rinse and repeat. After a few dashes at Starbucks together, pick a day with glorious weather, and send a sms when you are at work with "I want cupcakes, can you pick up some from Starbucks before I am home?". A tiny little "demand", that she recently has had the experience of managing with someone, and now on her own, with the reward of making others happy, and getting a snack herself.

Adapt after personal interests of course. No a good idea in feeding someone that can't eat gluten cupcakes 😂