Sage, I'm also on my own with my three kids but we don't have problems with covid right now. So I can only imagine the kind of stress you're under trying to manage the household. I often times also feel like everything is too much to bear. But there is no other option. We are the only stable parents in the house. The show must go on.
What I find helpful is to lower my own expectations of what a good mother should be. I've let go a lot on their academic performance - it was just impossible and damaging to my relationship with the kids when I kept the bar high. Instead I've made their state of mental health a priority. I always think of it this way - my H is an Ivy League grad. But look at him now!! I don't want my kids ending up like him. Also the other stuff too. My house is more messy that I'd like it to be, there's a lot of room of improvement. But I cut myself some slack way more than before.
Do more things for you, if possible. That's probably one of the hardest thing in this covid-era.
Regarding your H's suspicion issue, my H is similar. To this day he would still say things like "now you are free to go find a new man like you've always wanted." (which I've never said that) And I've stopped responding to him when he makes a comment like that. In the beginning I would try to explain myself, but now it really does not matter to me what he thinks. It is none of his business.
And I would add, be careful of the "I'm flatter that he cares" narrative. My guess is that it's not YOU that he cares, it is his ego. That is not a sign of love, it is sign of control, insecurity, maybe even guilt.