You need to be very careful here to not be drawn into a situation where your DD comes to you with everything she feels is wrong at her dad’s and you then take her side without question. Do bear in mind that it’s entirely possible that at some stage this could reverse and she could go to her dad when something you’ve done has annoyed her, and then you’ll be the one on the back foot, especially when she becomes a teenager.
It’s always worth bearing in mind that children can and do play their parents off against each other even when those parents are together, but it makes it so much easier when the parents are not and as such have differing ways of doing/reacting to things.
Reality here is that because you have only one child and your ex has three, the dynamic is going to be different in the two households from the start. You also have to bear in mind that while your DD is yours and your ex’s, so are the SM’s other two children. So whereas you have one child to consider, he has three.
In terms of expectation, she had a birthday party, I’m not sure what else she should have expected? Similarly a smart watch is quite a big present for a ten year old, even if it was bought from eBay. So again, I see no issues there.
WRT dropping DD off at school early this is something that perhaps your ex needs to look into e.g. whether breakfast club would be more appropriate at this stage. If the children are at different schools then it stands to reason that one of them would need to be dropped before the other. As your DD is the eldest then it makes sense that she would be the one to be dropped first. Added to which, she’ll be starting secondary soon and that won’t be an issue anyway as presumably she’ll be making her own way there and back.
In terms of clothes bought, you can’t compare a coat which is a necessity to everyday clothes which are not really. And complaining that he buys clothes in a charity shop doesn’t show you in a particularly good light. Lots of people use charity shops.
But your DD needs to be able to talk to her dad about things she feels are bothering her. Yes you can listen, but it’s not up to you to wade into their home and tell them how things should be done.
PS: I’m not a step parent, and i have an ex who absolutely prioritises his SD over our DS, but DS is old enough now to have made his own decisions on that score, I have never become involved in their family other than the time he cancelled his contact night because it was DSD’s birthday.
How his partner’s child is treated is none of my business. How ours is treated potentially is my business, but not in comparison to the DSD, those are separate issues.