Why does my MIL copy everything?

If you took her shopping it would need you to make the point of stopping being the identical things to me. I'll help you find things that look great on you instead.

Send her a picture of a tattoo you are getting to surprise dh... When she inevitably gets hers done just tell her you changed your mind...

You don't have to show her or tell her about your new stuff.

Stop fuming. It's bad for your health.

Laughter is good for you.

Start taking the piss instead and let it out. Roar with laughter at her next time she does it.

Feign concern. 'This is becoming a habit, MIL! Are you feeling ok?'

Start choosing a few unique things that can’t be replicated and take joy in them.

But mainly, enjoy the complement. A few people have given really good insight to the root of the behaviour. Better to feel sad that she needs to do it, than cross.

“Oh damn, we were laying bets on how long it would take you to buy the same thing. DH guessed four days and I guessed five.”

“Looks like DH lost the bet this time!”

”If I wanted to get away with a murder I think it would be pretty easy. I’d just do it in your neighbourhood. You’ve got the same hair as me, the same car as me, the same clothes, etc…. Everyone will assume I’m you.”

My MIL could never persuade her DH to spend any money on household things that she wanted (a very fraught marriage) but it was different if she told him WE needed something. He would spend freely on his beloved son!
Really bizarre. One Christmas we were given a brand new bedroom suite which we neither wanted nor liked. Had to look pleased and grateful! Next thing we knew the in laws had the identical one. She had obviously really really wanted that style for herself and once we had one she persuaded her husband it was worth them buying the same. Ditto a nest of tables, silver cutlery, you name it.

I have never worked that one out....it was always little things she wasn't "allowed" that were OK if we had the same first. Sort of a seal of approval. She never wanted things we chose, though, so not the same as you OP.
Maybe it was a confidence thing, although they were a couple who my DH remembered had a bare bulb in their sitting room for years because they had argued about what shade to get.

Offer to go shopping with her to choose some new stuff as you seem to like similar things.

This is so funny.
What an odd woman.
She is eccentric. Don't mind her.

You could say funny things, such as ..

I'm so glad you bought the boots just like mine; they look even better on you.

That dress is much better in size 20; it suits you.

I really am thrilled that you admire my style and bought that jacket.

Oh my God, we could be twins, you and me!

Look, my car had a baby. It's exactly the same DH, look!

You like it, MIL, well my perfume is Tiramisu Tuttotondo or Sugar Kisses by Lorenzo Pazzaglia but remember it smells different on different people's skin! (But keep the name of your real perfume a secret in brown paper packaging.)

I had a friend like this years ago. She copied EVERYTHING I got from clothes to cars to home decor. I always thought it stemmed from low self esteem and not knowing who she was or wanted to be. She came across as confident (more than me) but underneath I could see she struggled. Add to that the heaps of debt she amassed buying stuff to keep up with people, it's pretty clear now that she was just desperately trying to feel better. We are no longer friends (not to do with this) so I have no idea how she is now, but it was frustrating at the time. Stuff doesn't matter, but turning up at the same event with matching bags/shoes/hair was trying.

I’d not wear anything new in front of her when you know you are seeing her. Constantly wear the same old outfit and bag and keep your new stuff for when you know you won’t see her. She will soon get bored seeing you in the same old thing. As for the car can you sell it or part ex. If you buy anything new just don’t tell her or show her. Don’t feed her copying obsession.

What is she like more generally? Copying can be a sign of very low self-esteem, and a poor sense of self or identity. It can also be a neurodiverse trait (a form of masking). You said she is in an unhappy marriage, so perhaps her copying is a psychological attempt to "fit in" to your family.

I'd be hesitant to comment on this in a passive aggressive way until I had a clearer idea of her motivation. If she is generally a lovely woman who loves you both and is present and caring then I'd be tempted to let it go and I would choose to understand that it allows her to cope and function better. If she is generally mean and unkind then I would actually probably still not say anything. Someone having the same thing as me doesn't mean that I don't have it anymore and shouldn't take the shine off of it. Most things are produced in great numbers and lots and lots of people will have the same thing. I can understand why it would bother some people but it wouldn't bother me. If you do feel the need to talk to her about it don't reduce yourself by being snarky or passive aggressive. It's ok to raise this issue with warmth and kindness. "I've noticed that we have similar taste. Would you like to go shopping at the weekend and we can check out the handbags/scarves/shoes/perfumes together". Then you let/engineer that she chooses first. Give her choice lots of praise. It might be a case of building her confidence on her own choices and decision making.

My MIL can be a bit like this and immediately wants something that she sees others with (if she likes it) I know now it comes from not having much as a child to call her own and the security now of being able to buy the things she wants.

A lot of the times this comes up on here, it turns out, on further explanation, that the ‘copying’ is of very standard brands, clothes or children’s names. Are you saying she’s copying unusual or quirky furnitures or clothes, or is this the equivalent of those posts where someone fumes about their sister copying everything they do, only it turns out she just called her baby George and bought a silver Ford Fiesta?