So at least, you can agree that there is a kernel of truth to what they're saying.
I can only recall discussing workload one time with someone because
they asked what I had completed.
Ok, fine. Someone else asked you.
Either way, it doesn't really matter. Your managers want you to stop doing it, even if you did it only once and even if you were asked that question.
See it from the perspective of your managers. They don't really care about the details. They only want the behavior to stop.
And that's what they meant when they issued you with a "final written warning", it means they don't want to discuss this issue with you anymore. So either you comply with that request, or you go find a new employer somewhere else. They don't want to discuss this.
And maybe that's the real underlying problem that they have with you. It's not the fact that you did this, it's the fact that when they give you negative feedback and try to correct your behavior, that you respond defensively. And that might be the real reason they issued you with that final written warning.
I feel like there are double standards in my workplace
I'm sorry, but that argument is bullshit.
Your managers may not have cared about this behavior in the past, but apparently, they've changed their minds. They do have that right.
And if they do want to change this behavior at work, they do have to start reprimanding somebody to begin with. Their goal is not to reprimand everybody, their goal is to just stop the behavior from happening again.
Besides, even if they did reprimand others for the same thing, they don't have to tell you a thing about it. That's none of your business. These people are not your parents. They don't have to explain themselves to you.
And if you work in an "at-will" state, they don't even have to justify themselves to you if they fire you.
And you know what, maybe you're right. Maybe they do have it out for you. And right now, it seems like they're looking to make an example out of someone. So right now is not a good time to argue about the details of what happened, especially if they do have it out for you.
And if you want to tell them something, tell them that you received their message, that you understood it, and that you're going to comply with it. That's it, do not say anything else. And if they do want to fire someone to make an example out of, hopefully, once you're no longer trying to challenge them on those details, then they'll move on to someone else.
And in the meantime, if someone else asks you how much work you did, now you know what to say to them. You don't discuss it. Just say "I don't know."