I've had it with two jobs. Both times I was completely and utterly burnt out and beyond the limit of what I could do rather than any specific situation.
Anyway, both times in retrospect it had been building for a number of weeks. Dropping balls on fairly simple things, forgetting to reply to emails, remembering client appointments at the last minute or late despite them being in my diary, that sort of thing. It was also harder and harder to get up in the mornings, not from tiredness (although my sleep was becoming worse) but because I was desperate to stay safe in bed rather than having to face the world and the office. It got much much harder to make conversation with colleagues, even just general chit chat and my concentration during meetings was down to zero.
The crunch point, both times came completely at random. Sat at my desk (or wfh the second time) and staring at computer and suddenly just knew, without a shadow of a doubt that I could not do any work. Not didn't want to, physically couldn't. Couldn't open my email, couldn't carry on writing the sentence I was writing, couldn't just take a breather and go make a cup of tea and carry on, just....nothing. The very fact of being at work and trying to do anything or function was totally and utterly impossible. I didn't even feel panicked I just could not do it. It would be as if someone had sat me down in front of an airplane's controls and asked me to explain what they all did, completely incomprehensible.
Both times I managed to email my manager (telephone conversation out of the question) to say I had been taken ill, couldn't stay in work and needed to go home (or stop working when I was already wfh). As simple a message as that.
Then I got a GP appointment, explained how I'd been feeling, what had been going on and requested that I be signed off. I have a history of depression so am used to talking about my mental health and have a fantastic GP so the conversation was easy to have and I was signed off initially for 2 weeks, extended for longer after that time with another review with the GP. Another email to my manager explaining in brief what was going on, also explaining that at the moment talking on the phone was too difficult to do, attached a scanned copy of my fit note and that I would be in touch.
From the sounds of what you're posting OP it really sounds like you've reached that point. Stress and depression are killers. Please do get to your GP and get signed off. Need only be a couple of weeks initially, take some time to breathe. Working out what to do next to change the situation can come later. I came home from the doctors, arranged childcare (single parent) and slept for nearly 36 hours. The relief of not having to put on my armour and struggle through another work day was incredible.
Your work might not like it if they're not usually sympathetic about sickness, but there's nothing they can do about it. You are protected. And mental ill health should be taken just as seriously as physical. They may surprise you, in this Covid era and the new focus on self care and mental well-being there is more acceptance and recognition that thousands upon thousands of people right now are struggling and need to take care of themselves.
Do take care OP and I really hope you are feeling better soon