It's not an annoying question at all, it's a sensible one! I wasted money on rubbish toys in the past just seeing them online and not realising some were unsafe or unsuitable.
I'm a big fan of the large cork logs - they are good for a natural theme but also they just make good things in a cage for any hamster I think. They are light so don't sink in the substrate if it's deep. They have an interesting texture and make a climbing element for hamsters to climb over, and they make a nice big dark tunnel (no issues with hamsters getting stuck in tubes that are too small). I have also used them instead of a ramp up to a platform - eg on top of the substrate and partly under the platform kind of wedged under it - so it makes a ramp and also a tunnel under the platform.
I have two shorter ones in our Syrian's cage. Those are German sold ones though and most tend to be longer so you'd probably only want one if it's a longer one. I also like the cork bark pieces which can just sit on top of the substrate or be layered to make steps or to stand something on.
Other natural things are terracotta (eg plant pots or plant pot bases). A plant pot base on a shelf can sit under a water bottle to catch drips and also be big enough to be a large open food dish. And it's somewhere to sit and cool off in hot weather.
Those items tend to be too heavy to have on the substrate and are better on a platform, although a small plant pot on it's side could make a good hidey place on the substrate where it isn't deep enough to be tunneled under (or it can squash them).
You can buy sprays of millet which are safe to eat and sometimes enjoyed by hamsters (some love it, some ignore it) and stick those in the substrate or in the cork pieces, to look like plantlife or little trees.
Some people also have a fenced off sand area or large sand box, rather than a sand bath. Substrate wise though I would stick to conventional substrates and not be tempted to use things like moss or peat as those can encourage damp and mould growth.
Cork can be quite dirty/dusty on arrival but a bit of a brush and rinse and let it dry out naturally and it's fine. It can be an idea to freeze or bake cork or natural wood to be sure it's sterile and nothing living in it. Although I believe the wood is sold as sterilised - but you can't always tell. I tend to freeze cork items for a week.
I'll have a look on Amazon.com for other suggestions.
https://www.amazon.com/Zoo-Med-Natur...ark+half+round
Vine branch (you have to check for sharp points or edges with these but can snip off any sharp bits or use a bit of sanding paper on them).
https://www.amazon.com/Koyal-Wholesa...eywords=branch
https://www.amazon.com/Pack-Zoo-Med-...rk+bark+pieces
These are popular with our hamsters - natural and chewable and soft (no sharp bits) but i think they're imported to the US as cost a bit more
https://www.amazon.com/Rosewood-Pet-...yacinth+tunnel
This is the same stuff only a mat - could be used on a platform
https://www.amazon.com/Rosewood-Pet-...yacinth+tunnel
Millet sprays
https://www.amazon.com/F-M-Browns-42...s=millet+spray
https://www.amazon.com/New-England-P...a+plant+saucer
Coconut huts can be popular extra hides. This one looks to have a large enough entrance hole (needs to be 6cm diameter or more for a syrian).
https://www.amazon.com/SunGrow-Cocon...D58RJNF47BT7TQ
Bendy bridges and other bark items are popular - but watch out for nails on any bark houses. I also freeze bark items for a week before using (just to make sure anything that might be living in them is dead!)
On the freezing topic - I also freeze all bags of hamster food for a week before using (have one on the go and one in the freezer) after having an outbreak of pantry moths.
IT could add up expensive buying a few things, but you can maybe get 2 or 3 things and improvise with the rest. Cardboard shoe boxes make a good house - cut the base out and keep the lid as a lift off roof to check inside and cut a hole for a door - you could have it as a subterranean house with mostly just the roof showing and items on the roof (or a chill n chew mat on the roof). You just channel a bit of substrate out down to the entrance.
Cardboard kitchen roll inner tubes slit down the side also. Maybe not so natural looking but cardboard is good for them to shred and chew.