this is.... unhealthy. i know this was a personal rant but... it made ME stressed out.
it's seriously just a nice sentiment. if you're not feeling well at all, just say something dismissive. when i'm not having a good day i'll still say "i'm doing alright, thank you for asking." it's a simple way to ensure the conversation flows and you're able to get them out of the window/door relatively fast.
your energy is misplaced and i think it's important to reflect on what it is that bothers you the most. it seems to me that you're more upset with the lack of covid-19 precautions, and people being sick. put your frustrations on those who do not care for preventative measures, not customers who are just trying to be nice. that's all.
also, i just don't think it's much your business at all to know if a coworker is lying or not. it can be stressful to run 3 mans or 4 man plays, but would you rather that or a coworker who IS sick, or just feeling sluggish today and would be less productive?
i think you've got a lot of pent up frustration towards the job itself and that's an unhealthy way of going about it. maybe look into finding a different job to help calm you down a bit, considering.
i wish you a genuine good night and i hope things work out for you

People don't actually want to know how you are though. It's just the polite version of our culture's greeting. "Hi how are you?" is considered more polite than just "hi". Just realize that someone is trying to treat you like a human. And not all your customers are going to bother, so don't be mean to the kind ones.

You can follow the script and say you're fine. Or you can be kind but honest. Say you're so busy today. Say you're tired. That's fine. You don't have to lie, but you also don't have to share all your work trauma with everyone who asks how you are.

I'm sorry you're having a rough time. Starbucks is becoming an increasingly unpleasant place to work.