I had something similar happen recently. I was let go for being "not a good fit" after two years. Then my boss told me he would fire me on the spot and not give me any severance if I didn't convince the team that I was leaving on my own. He told me "in the interest of psychological safety" I needed to convince everyone this was my choice and wanted me to send out a message (that he wrote) about how much I loved the place and would be "cheering for their success" after I left. 

It was only in recent months that I became aware that I am the third person who has been hired in my role and then let go for "not being the right fit" since summer of 2020. 

It was a terrible position that was impacting my mental health, so other than missing the paycheck, it's not all bad. 

The kicker for my boss is that the person who reported to me quit a month or so after I supposedly left by choice. She'd only been there for a little over a year, but left because she didn't see "any growth potential", which I shared with him. I had also argued that she get a big raise, which she did get. So, now he looks like almost the entire team decided to leave at once, me with no place to go. But, he's one of the least emotionally intelligent people I've ever met, so serves him right. He's one of the company founders, so I imagine he will "retire" soon and just continue to collect equity. 

The thing about US employment law is that it gives employers so many loopholes that they can basically get rid of you for no reason and be protected. 
 

A lot of companies fire people in the wrong way. Not enough notice, No  written warnings, No  meeting to help the employee. ,  No, written  plans ,, to  help the person to do a better job.  

Are they allowing other people to do what they are saying it's not in the company laws, was there a employeee information packet out linking company rules. Or they making rules to fit there case.  You should of been given a employee handbook out line time off, how to get time off.   Who has to approve it, how far in advance it's needed .  
 

Sueing them, unless it's a big company [ US post office, IRS, state jobs], will get you money but not your job back.  Better to be in a job where it's fun to work at then ones that you hate to go to. 
'Makes for a better life and less medical problems. Best of luck 

You should talk to a lawyer but you may need to accept that sometimes there just isn't much that we can really do.

I personally think that the only real issue you have to go after them for is the possibility that they fired you in retaliation for your attempting to file for FMLA.

I think the PTO issue is probably double edged.. you do know you took time off without permission.. most companies can and do terminate for that alone.. and if they can show any other support.. they will likely prevail on that alone.. if you are going for wrongful termination for taking PTO.

BUT.. they did not appear to respond in the appropriate time to your FMLA request.  They owed you a YES or a NO.. if they said NO.. and you felt that the reason they declined was not legal.. that also gives you some weight to them not honoring that.  But.. is your company required to offer FMLA (not all are).?  

Unless required by law or in their company procedures/contract with you... they didn't have to give you notice.  they don't have to pay PTO.. they don't have to have a "good" reason to let you go.. as long as they don't terminate for a protected class reason.. or as retaliation for filing FMLA.  I mean.. yeah.. most decent employers will pay out earned PTO.. they will give workers notice in a layoff..but they don't necessarily have to and some won't.. you apparently worked for a crappy company.  And.. it appears you were NOT the only one that was let go... you said others were basically let go as well.. it was just in your case not communicated well...

So, by all means go speak to a lawyer to set your mind at rest over whether it is even worth your while to pursue anything against them. 

In the end, it's often difficult to prove things.  I have a feeling that they let you go because you were not working out for them.  Your boss didn't like you for some reason.. and you, yourself, even basically told them that the job was too much for you when you tried to apply for FMLA due to job stress.  They already had to make cuts.. and you made it easy enough for them by taking time off without permission.. even though it's possible they set up that scenario in order to give themselves a concrete reason.  In hindsight.. I would have gone above my manager's head to deal with the FMLA and time off issues before I took the time off.. but the reality was that in that situation.. this was not the right place for you and you would have been well off to already be looking.. since your manager was clearly viewing you as a problem for some reason.

But.. perhaps with the FMLA issue.. a lawyer might be able to prompt them into some kind of settlement.. because it does appear they did not follow the rules when it came to that process.. and possibly retaliated towards you.  I hope you have concrete proof of your offical request.. that should make it fairly easy for a lawyer to prompt them to offer some settlement.