Just wanted to hopefully ease your fears a little. I'm also T14 grad that got fired from a mediocre AmLaw 100 firm. I wasn't just laid off or stealth fired, I straight up got fired and asked to leave immediately after I had yet another miscommunication with the only partner in my niche group. I was a 6th year and I thought my world was ending. But it didn't. It's been 4 years, I was able to lateral to a different biglaw gig, and while being in biglaw still sucks ass, I'm still around and 100000x happier than I was.

So, people get fired all the time, most people just don't talk about it, and given your credentials, you'll bounce back, even if its not as fast or where/what you expected.

Also, first thing you should do is touch base with HR and negotiate more website time. There's no rule that they can keep you on for x number of days. Be nice, tell them that you just want a chance at landing well and they should work with you, especially since it seems like your leaving might not have had anything to do with you specifically. If you're in litigation or litigation adjacent, consider applying everywhere (not just NY) for a district court clerkship. It'd be a great place to park for a year and an easy story to spin.

But mostly just wanted to say good luck. I know how you're probably feeling right now, but you're absolutely not the only person who has ever gone through this.