There are a lot of solutions to things that cost money that in my opinion are the "good enough" options. For example: Costco prepared meals or frozen meals as a substitute for takeout. It would be cheaper to make the meals from scratch, but way more expensive to get it as takeout. I should have been more open to solutions like this.
This. Don't worry about optimizing. Give yourself grace, understand things will get better and you'll have a bit more bandwidth. For now, just try to do a little bit "better" instead of perfect. Buy the frozen pizza ($$) instead of takeout ($$$) or making from scratch ($). Figure out halfway solutions. Maybe you buy prepared food at the supermarket for lunches that's better than takeout but not as good as making from scratch. (Although do try to make coffee at home - maybe make it the night before and microwave to warm up?) Keep snacks in the car or office, buy in bulk so you just need to bring them in once for a week or two, make it easy so you don't have to work hard to stretch your frugality muscle. Re shopping, make yourself not buy anything unless you've thought about it for X hours. (24? 48? a week?) That usually curbs my impulse and lets me think about if I really need something.
100% this
I went through an insanely expensive few years with serious health issues and doing grad school, and that's survival mode.
Also, when it comes to food, I hire someone to bulk cook for us. It costs us $60-100/wk. I print out very clear instructions and within a few hours, I have a week's worth of nutritional meals portioned out in the fridge. I find this much, much better value than just about any other source of food convenience out there.
It took several weeks for my kitchen helper to get to the point that she could do it all by herself, so for the first while I had to supervise and do some of the work myself, but she got there and now I don't even stick around while she's cooking. We go out for a walk or a coffee to recharge and come back to ALL THE FOOD.
Also, invest in some mental health supports.
As for your savings rate, the only person shaming you for that being low right now is you. No one is pressuring you to save more than your circumstances allow, that's a pressure you are making up for yourself.
Focus now on figuring out what a sustainable, healthy life looks and feels like, and strategize how to work towards that. When life changes drastically, you need to not stay too attached to old metrics of success. Be nimble, adaptive, and perhaps develop more robust metrics of what success actually means to you.
Remember, one of the number one predictors of good outcomes for kids is that their mom is happy and healthy. Not that she saved a sht ton of money.
Money has to serve the goal of happiness and health, not make that worse.