I went through a similar situation about a year ago. Was burned out at work and my workplace had gotten increasingly toxic in our post-IPO world. I went on medical leave and short-term disability for 3-4 months, and used that time to work on feeling normal again, and on looking for a different job.
If I were you, I would...
1) continue meeting with a doctor regularly to discuss treatment options. That could be short-term benzo use, antidepressants, lifestyle changes, as well as going on medical leave. Regular visits also help build up your rapport with your doctor and create a record that you've been seeking help for these issues. Those can be really helpful in the future. For reference, I was seeing my doctor weekly when going through my situation.
2) don't tell anybody at your work that you're experience burnout until you absolutely have to. And even then, limit it to those that need to know (which, likely, is HR and not your manager or coworkers). I've seen a lot of friends be passed over for promotions or interesting projects or even let go after disclosing mental health issues, even for things as prevalent as burnout. Figure out a plan with your doctor first, and then follow your doctor's suggestions on who to contact at work.
3) seriously consider time off, either through a week of PTO or through a more extended medical leave. Yes, it's a pandemic, and yes, you may not have any idea what you do. But, honestly, that's exactly why you need time off. You'll get bored and figure out what you like to do, and that'll open some probably-currently-blocked mental doors on things that might improve your life. For me, I went on a road trip through the southern US and visited national parks I had never been to before. All outdoors, nobody around, never went to restaurants, and brought an air purifier for my hotel room or airbnb. I've also started booking week-long stays at neat AirBnBs with no plans whatsoever... just read, hike around, journal. And even though it feels boring, it's incredibly reinvigorating. But when we're burned out, we forget the things that we love because we're so burdened by our jobs.
4) seriously consider a new job. Another cause of burnout is breakdown in the feedback loop of our work. So we put tons of effort into something, only to shift priorities and not finish a project... or only to have the project handed off to some other team for nebulous reasons... or only to have execs abruptly nix the project... etc. If that resonates, then maybe part of the issue is you're not getting what you need from your job, and it's time to look for something else.
5) double down on self-care. You probably have heard all of the things before: have a consistent sleep schedule, remove screens from your bedroom, go outside, exercise every day, cut down on sugar/alcohol/caffeine, have regular social contact (safely, but FaceTime, etc), reduce your social media usage, meditate, journal, etc. Cultivate hobbies -- what about learning a new language, or learning the guitar, or starting a garden, or learning 5 new gourmet meals to cook.
These issues are really common in tech, and right now life is particularly hard. There's a lot of instability in the world, there's not a lot of things to do with free time, and so we work too hard with nothing to look forward to. It all sucks. But it's great that you've recognized you're not in a great place, as that's the most important first step :)