Your post made me laugh op. My 3yo dd has had many moments just like this. I feel your pain. She's also 'strong willed' and a powerhouse of emotions. Now she's verbal it's gotten quite funny. She's said the same thing before, No mummy we're NOT best friends! No, I'm NOT happy about this! No mummy, it's NOT so cool! (Last one said when trying to distract her by looking at something.)
I use a range of tactics.
Sometimes I just ignore her completely; stay close so I know she's safe, but just let her have it out. Don't react. Other times I talk gently to her, try to tell her how it makes me feel to see her this way. Oh no, Mummy wants xxx to be happy not sad etc and I pull a sad face. Sometimes this is enough and she collects herself and wants to hug it out. This one doesn't always work though!
Sometimes I just quickly say stuff for example oh quick, look over there! I see lunagirl! Gasp! Come on we need to pay for the cupcake to save the day! Time to be cupcake heroes! Suddenly she will be in a fantasy land playing pj masks/paw patrol etc. There's endless scenarios with this one. I look mad Also I sometimes distract her by asking her to do silly fun things. Can you do this (breathe in and out a few times/make a fish face/count to 5/wiggle nose) she usually enjoys this and it gets her laughing again. not mad, insane, I look insane
Counting to 3 also works now, at last. If we get to 3 she is timed out. She doesn't like being timed out, mainly because she's getting no attention, and she LIVES for attention. She knows we are serious and follow through with everything we say. So it's enough of a deterrent. After the time out we always discuss/say sorry/hug. I had to practice this a lot at home before it worked outside though. It wasn't until she turned 3yo that it worked actually. Nothing got through to her before then! Now I rarely even make it to 2 when counting.
Also if we are out I sometimes calmly tell her if she keeps doing whatever it is she's doing then she will have to go back to the car and go straight home. (I only say this when it's actually feasible to do it.) As we have followed it through every time, again, she knows we mean it and now it's usually enough just to say it. I don't always feel like Mary jeffing Poppins so there's been a fair few occasions where the kicking/screaming variety of tantrum was clearly not going to relent, so she's been picked up and taken straight home, no questions.
I'm no expert btw and have no idea if I'm doing right or wrong here, just felt my way along. Maybe these examples will help you.
I really feel for you. It's all normal stuff, but can be so exhausting! They can be so full of emotions that are too overwhelming for their little minds and bodies. These are tough years.