The phase won't have passed before your new baby is born, no.
I sympathise with how you feel.
She's just a little girl and she doesn't have a fully developed sense of empathy yet. I know it might feel like there is more going on, but it's just a young girl practicing at being an adult. She will be observing your responses and it will form part of her development.
I am a step mother too. A pregnant one. And one of my step daughters is 10. Believe me, I do get it.
10 is a very funny little age for them. They're navigating that little jump from childhood to double-digits. It can be painful to go through with them.
The bit that really stings, and I know you have it too because you used an example in your OP, is when they say "my mum does it like..."
For example, did you know that I ball socks "wrong"? There are, apparently, right ways and wrong ways to ball socks. And I get it so wrong that they had to tell me, and explain how their mother does it. And they weren't very nice about it! 😅
And no matter how thick our skin gets, it still nicks at us. (It even still nicks at me, and I've been at this for a while! 💁🏻♀️)
Always remember that their mum is a role model to them and it doesn't mean they're trying to compare you or wind you up. Your step daughter is just sharing her view with you. Her view is mostly made up of what she witnesses her mum doing.
I do tell my step children when I feel hurt by something they have said. I never bring their mother into it. I don't escalate it to my husband unless it needs to be. And I always move on after it's been dealt with.
Example:
"Yeah, I guess I do roll my socks differently. But it doesn't matter. It's a small thing. I don't know if you noticed but you didn't talk to me very politely then! I don't mind this time, but don't make a habit out of it. And always think before you speak to anyone like that, because you could end up really upsetting someone!"
Make it unemotional, make it about them, make it a life lesson and don't snap "I bet your mum told you to say that?"
Then I don't mention it again unless they repeat the behaviour. Kids don't need someone stringing it out. They just don't get it and it's better to deal with infractions as they arise, and not broadly and holistically.
Keep your husband informed on how you feel. But, it might be an unrealistic expectation to have him talking to his daughter about this, for the reason I outlined above. Better if he witnesses it and deals with the instances as they crop up.
One other thing is that pregnancy makes all of this so much worse. The hormones. The aches. The tiredness. The very loud ticking clock, in your brain, counting down until everything changes...
When your baby is born, your step daughter is going to be hovering around wanting to show you how grown up she is. It might do your head in a bit. But you're going to suddenly feel a lot more confident in dealing with it all.
And your step daughter is going to give your new baby bottles and bring you fresh muslins and be the first one at the side of the Moses basket when baby cries.
And you'll be watching her holding your new baby and you'll realise how tiny they both are and how much love there is between the two siblings. And your heart will burst and you will (I promise, promise, promise) feel so much better about it all.
It's big changes for everyone. Congratulations again on your growing family. Try to relax and let your SD navigate this weird phase without getting too upset by it.
Nb. If all else fails, tune out. Last week when my step son said my soup tasted like "a dog's butt hole" I mentally quit. I went into the utility room, balled some socks and played the Meh Na Meh Nah song from the Muppets over and over again in my head.
The Meh Na Meh Na song has honestly saved my marriage on at least 25 separate occasions.