You fucked up by saying you would take her shopping, and now that is the precident you set without ever meeting this person. You will never win this situation... EVER
It was implyed you would be her sugar daddy just by liking her so you never needed to address it unless she did, in which case that could have been done in person and now you have zero leverage.
This dumbass will not put out for you, because you fucked up your role in the situation which was to be a daddy of sorts and daddys dont just give their kids what ever they want when ever they want it, they got to earn that.
Change shopping plans to dinner and dont waste your money on terrible prospected people in your life.
Theres nothing wrong with buying people you want to be around lovely things, but you cant just be someone to take from.
Its meant to be a two way street and that needs to be earned.
Just like she more than likely wont put out on the first date, neither should you.
Its a respect thing and believe me Millenials have a weird sense of entitlement but respect boundaries without being aware of it.
If she doesnt spend the entire time on her phone, shes a keeper.
If she spends any time on her phone, you are just being suckered.
You dont need what shes offering as much as she needs what you do. She wants a real man that can afford to buy her things and be a father like figure that is stronger than the boys shes use to being with.
Otherwise shes just a prostitute and if thats the case, just offer her cash, but shes not looking for that, she wants more than that more than likely.
Have fun, but boundaries are good for everyone