The walnut is probably a special thing and she can't crack it (the shells are quite big and hard) so she's hanging on to it. How often do you clean her out? I'm just wondering if at some point her food hoard was removed completely during a clean out and she's now looking for a safe place to hoard food so is putting it in her bowl and adding to what's there - if that makes sense.
Hoarding is quite an important instinctive natural behaviour, and it can go a bit skewiff if they feel it might be "stolen".
If they have a house that is open underneath and sat on top of the substrate, they tend to bury hoards underneath their nest, hoard most of the food and then eat in their house from the hoard (like breakfast in bed).
So maybe there's something in her cage set up that isn't quite working for her - that and maybe too much cleaning out?
It isn't necessary to clean everything out once a week as pet shops advise sometimes. You can mainly just "spot clean" any smelly or soiled areas and if you provide a litter tray she will probably use it - if you put it in the area she normally pees, which is often a corner of the cage. With spot cleaning you just take a handful of the wee'd on substrate out, add another handful, and mix it in so it smells a bit familiar. They can get quite confused and stressed if all their familiar scent is taken away at the same time (ie full cage clean).
If you have the substrate deep enough (min 3 to 4" but ideally 4 to 6") and use a litter tray and spot clean if necessary (the cage should stay clean if she uses the litter tray) you can easily go 2 to 3 months without replacing all the substrate, and even then it's good to replace a bit of the clean old stuff and sprinkle it on top or mix it in so it smells familiar. And to clean any other things at a different time - eg wheel one week, toys another week etc. That way something always smells familiar and they feel more secure.
Also when doing substrate cleans, leave the nest and hoard unless they are pee'd on. A dry hoard can be left for really quite a long time and then if it starts taking over a bit you could prune it back and remove some of the older food. But if you ever remove any hoard you should always put some new hamster mix back in exactly the same place or they do start getting abnormal behaviours if they think some predator has stolen their hoard!
Not sure what cage you have or how it's set up, but I'd suggest
1) Add more substrate and mix it in, if it's not very deep
2) Give her a house that is open underneath and sat on top ofthe substrate - a shoebox is ideal - cut the bottom out and cut a hole in for a door and keep the lid asa lift-off roof so you can check inside without needing to take the house out and the nest falling apart. The roof also makes something to sit on. If you put a bendy bridge tunnel over the door it also makes it dark inside and gives a ramp up to the roof. They do need somewhere dark to retreat to and something big enough to build a large enough nest.
3) Put a big pile of torn up strips of plain white toilet paper in a heap in the cage somewhere (not in the house) and she will take what she wants to build or rebuild her nest in the house. Keep her old nest and put it in the house along with some food in one corner and maybe a treat to tempt her in there - eg a small piece of apple.
4) Keep putting hamster mix in her food bowl but maybe half as much (a level tablespoonful eg) and scatter the other half on the substrate so she can forage for it. If she starts foraging, the instinct to hoard in her nest may kick in as well.
5) I wouldn't empty the food bowl for a week, just keep adding a bit and scattering the rest every day. Then empty it out after a week and refill it. This should give her time to adjust to not using the food bowl as a hoard.
6) If she continues to use the food bowl for hoarding, then just do scatter feeding - about a level tablespoon every day just scattered around on the substrate. Then see what happens over the next 2 or 3 weeks. She should settle into a routine once she has built a nest in the house and there hasn't been any cleaning for a while.
Apologies if you know all this already. If you don't have a shoe box or don't like the idea of a shoebox house, this house is quite good for a Syrian hamster - it's far too small for a guinea pig and a good size for a Syrian. It doesn't have any nails and has a lift off roof. The door is quite large so putting a bendy bridge tunnel over the door should tempt her in there.
https://www.amazon.co.uk/Ferplast-Gu...sin+guinea+pig
Some people paint wood houses inside with plastikote so it's wipe clean in case it gets peed in. You don't have to and I often haven't if our hamster is toilet trained. It's quite a breathable house as well so won't get condensation building up in it. This is the plastikote - it's water based and pet safe and doesn't smell of anything really. A coat is dry in a couple of hours.
https://www.amazon.co.uk/gp/product/...?ie=UTF8&psc=1
You can use anything as a litter tray really but I like these corner ones - they're big enough for Syrians. Our hamsters have always peed in the back corner (which is a bit higher) and sat in the front part for a wash.
https://www.amazon.co.uk/Hamster-cor...=hamster+potty
Most people put chinchilla bathing sand in which soaks up the pee. You then just empty the litter tray every 5 days or so and wash it out and add new sand. They usually use it if you put it in their chosen pee place but if you put it anywhere else they won't use it! The cage then hardly needs any cleaning. Their poops aren't dirty or smelly, they're like hard little black seeds and hamsters sometimes eat or hoard their poops (which is normal) to get extra nutrients. They have two stomachs and can redigest nutrients from the poops. So don't worry about cleaning out poops unless they start to take over in a big way. If you remove all the poops it also stresses them as that is their emergency food supply.
They can get some funny behaviours with hoards and may hoard in more than one place or move the hoard if it's been disturbed. Best not to remove it unless it gets pee'd on as they can then start hoarding in their toilet and peeing on the hoard to deter others from stealing it. Then it gets into a vicious circle as then you have to chuck the pee'd on hoard so they keep peeing on it! If that happens I put new food back next to the toilet area and eventually it breaks the habit.
You might find she does have some hoard buried right at the bottom of the cage. But if her hoard has been cleaned out and thrown away regularly she may just not feel safe burying hoards and just puts the food back in the bowl.
Hope that helps a bit! It would be better to give half a shelled walnut - I get the little snack packs from the supermarket. Half a brazil nut is good too. You can give shelled monkey nuts as they can crack those and enjoy doing it. If you use Tiny friends Harry Hamster it has monkey nuts in anyway.