How to deal with lying - any advice?

[Yellowfish2020]

11 year old step daughter just can't stop lying. She's only recently come to live with us full time as her mother is just not able to offer her a safe upbringing (social services and courts all agree). She's great, we have fun, but she lies about everything, even things that are unimportant and clearly won't get her in trouble.
I'm not sure how to handle this, whether we do damage by being too heavy handed, but equally we have tried the softly and understanding approach.
This morning she lied that she had eaten breakfast. Previously it was that she was wearing new trousers not the ones from yesterday and that she didn't know how yesterday's must have got back on the hanger. So it's stupid stuff, inconsequential. And that's what bothers me. She will look you in the eye and say black is white. Over nothing. This is also a trait of her mothers who has real mental health issues.
Her one 'thing' is PlayStation. Her dad is all in favour of taking all screen access from her. At a loss as to what else to do. Have tried to explain and articulate why truth and trusting relationships are important- but it doesn't make a difference. Some of the stuff she's lying about is really odd - saying she is wearing black trousers when they are grey (this is not a vision thing - there is a clear difference) and I just don't know what to do. As a step parent without my o an kids, I'm not sure how unusual this is and how to deal with it.
It does seem 'wilful' so understand the punishment approach - but it's the 'type' of lie that seems more like a much younger child that worries me

Has she ever had any support/counselling for what she went through with her mum? I can’t imagine it was plain sailing if SS think she shouldn’t be there.

She does at school with an emotional support worker who has been great and said she's doing really well. School say all her work, relationships, everything is flourishing. A lot of the stuff with her mum she is not aware of (we have kept her as away from it as we can), but I do understand that there may well be an impact as it's a big thing.

She’ll probably know more than you think she does. I’m no expert and my DC are too little to have learned how to lie but I’m an adoptive parent so know some of the issues that come with SS involvement. If I were you, I’d be looking at some counselling and possibly some life story work.

Lying could be a form of control. I imagine things feel massively out of control for her right now and lies can help regain that. The lies wont be done deliberately or to be manipulative it is a survival technique.
I really really recommend the A-Z of therapeutic parenting by Sarah Naish. It's literally is an A-z of ways to support children through different issues and there is a section on lying.

I think she could be using this behaviour to test if she's loved, secure and accepted. She's probably feeling unsettled after her DM's problems and is testing the water.

Thanks for the advice everyone. I agree it feels like controlling or testing behaviour and no doubt linked to what she's been through. We will all keep working through it.