You seem like a highly self-driven motivated individual. And you are here asking for help/advise. You are already doing better than most others in your situation. You will be fine don't worry about your career.

You are 100% right. You need a break. You have earned some goodwill with your founders. Encash that – slow down and take a short break (couple of weeks) to clear your mind of the stress. Maybe leisurely travel will help. Spend this time outdoors in sunlight and with non-tech friends (or strangers).

Then come back to begin the repair at work. In your burnout state, you may have become impatient and rubbed people the wrong way. Time to repair that damage. Get into a 'enable and support others' mindset rather than 'get sh*t done, carry the weight of the world' mindset. Focus on people rather than things. Master patience and keep calm. Slow down. Consider things carefully, slowly, with other people in the center and enable others to do things, slowly.

Set your expectations with your team lead - that you want to change into slower gears and focus more on helping others rather than taking on everything yourself.

Don't worry about performance ratings etc. In the long run it doesn't really matter. (I know it is hard to believe this. Have to take it on faith). Also, don't worry about the startup or your project. They will do just fine without you carrying all the weight. You may not see it that way now, but don't worry about that. It's 'above your pay grade', really.

Within a couple of months, things will be back to normal and maybe better than normal. Then you can slowly ease back to unleashing your full brain power to solve unsolvable problems like X. But keep the focus on helping other people. Don't take the pressure all on yourself.

This may sound simple. But it can be hard sometimes to do simple things. If you master this, your team lead or anyone cannot play politics and screw with your head. Small slips and nitpiks by anyone will be just that, and won't bother you anymore. Also, take the time to showcase your work and get the positive recognition. Don't just keep chugging along without paying attention to organizational stuff. This stuff matters.

Once you are in a good place and feeling confident, re-evaluate your situation and take action.

Hope this helps. Good luck.

p.s: On your personal front, fixing a 20-minute free-body floor exercise routine at home (don't have to go anywhere), with a fixed/early wake-up and sleep time and fixing your stomach (good food) will do wonders to your mental state. Take care of yourself. It will payoff big time.

p.p.s: What's the worst case scenario here - getting fired? That is not the end of the world. Hopefully, you have enough savings to survive a couple of months - to recover and get to interviews in a more calmer and confident state and land another job. No matter what, believe in yourself.

Finally, hopefully you won't put yourself in similar burnout situation, in the future, for anyone. Nobody does well in a high-pressure situation for too long. Many times we create these pressure situations for ourselves. It doesn't help us do our best work. Find your optimal fuel-air mixture and burn rate.

I've assumed a lot about your situation – I may be totally spot on or completely wrong. Likely somewhere in the middle. YMMV.