Well done for rescuing her, the cage you've given her is by far much better than the one she was in, however I hate to be the person to tell you this, but the minimum floor space for a Syrian hamster is 100cm x 50cm x 45cm depth (depth can be adapted slightly this is more a guidance to avoid escaping hamsters)
Don't get me wrong you've done a great thing in taking her home, however I would consider looking to upgrade her home as soon as you can. A very easy way to upgrade a hamsters home is DIY bin cages, give these a google or YouTube search and you can find what these are but essentially they're storage bins turned into hamster homes by meshing over the lid.
Or there's plenty of Ikea hacked hamster cages on YouTube to have a look at. When I was looking for my Syrian, I found that DIY cages gave a lot more space for less money to larger commercial ones, however it is possible to get the large ones just ensure the bars are small enough, it's surprising the gaps they can squeeze through.
In terms of her using the wheel, what inch is the wheel? Due to Syrians size, anything smaller than an 8 inch wheel arches their back into uncormfortable positions, and therefore discourages them to use the wheel. Ideally the wheel should be 10 or 12 inch. This is a great option Trixie Exercise Wheel, 28 cm Dia... https://www.amazon.co.uk/dp/B00365P9NY?ref=yo_pop_ma_share
As it's rather cheap for the size that you get, and considering it's not sold to be silent, I find this wheel rather quiet, and my Syrian is in my bedroom.
Don't worry too much about her being active in the day, it could be that where you found her always had security lights on, and so she could never distinguish when day and night was, or that she found day time more entertaining watching people and that due to lack of entertainment at night for her.
I don't want this post to sound like I'm nagging, I just wanted to inform you of a few things. I hope you enjoy your new little friend. My Syrian Nala is such a character and it's so funny to sit and watch them do their thing 😊
I currently have 6 hamsters and 2 guinea pigs. I used to have 8 hamsters but Humphrey died last year at 4.5 years of age, and Aldi died year before that at 3.5 years.
IKEA is where I get my hamster houses from. There are many IKEA homes for hamsters online if you search. People make hamster homes from furnitures.
All my hamsters run all night long on their wheels, and they are quietly sleeping during the day.
Your hamster is exploring her new cage, which is perfectly normal.
My 6 hamsters all live in separate cages. They all exchange cages after a big clean up, and they go explore their new cages every time. After they know where everything is like their water bottles, food bowl, treats, new toys, and etc. they all just settle down and go to sleep and/or run on their wheels depending on the time of the day,
Maybe for her safety, have a look into making a cage that doesn't have bars she can climb up or squeeze through. She may be slightly stressed as she doesn't know what to do with the space. Before you found her you don't know how long she was on that tiny cage for, she wouldn't know any different
I would give her some time to settle in. New environment could be intimidating for her.
I thought I share a photo of my Ben the hamster, who has had fair share of exotic vet visits due to eye infections, but currently doing very well. Ben is about 3 years old. Ben has a big IKEA cage he has all to himself. He sleeps during the day, and only comes out to eat treats. He loves running on his wheels all night long.
We keep saying our dwarf hamster doesn't know what hamsters are supposed to do. She also sleeps out in the open (kind of wherever she happens to be... on the wheel, in the food dish, next to her house, etc.) She doesn't seem to know she's supposed to be nocturnal. Her wake/sleep times seem pretty random. She's strange that way!
We had a really big female hamster... we have a picture of her next to our baby guinea pig because they seriously were about the same size. Our current one is much smaller. I think there is just a range of sizes, just like dogs/cats/humans.