I’ve kept button quail as well as finches, and my friend has coturnix! These suggestions are very thorough and you probably already know a lot of them, but for people who might not I’ll include them.
Grow them some wheat grass (either hydroponically or with a safe organic medium) in a tray, so they have some grass to nibble and nestle in!
Hang fake plant vines in their enclosure to create curtains and different environments. You can use the ones from the pet store or from the craft/dollar store, but if you use the ones from the craft or dollar store, washing them very well in a vinegar solution and rinse thoroughly to cleanse them of preservative, and avoid any with foam accents or glitter or anything like that that they could peck off. Also, if the color runs, don’t use them.
You can use real plants, small potted plants, if they’re safe to nibble! I cover the soil with smooth river rocks (like sold for fish) so they can’t access it. You could also make sure the soil is bird-safe and plant grass in the bottom. (This generally requires a pretty big cage, obviously.) Some safe and fun to perch in options include ferns, spider plant (Chlorophytum comosum), or small palms like kentia (Howea forsteriana), lady palm (Rhapis excelsa), or ponytail palm (Beaucarnea recurvata). However, make sure they’re organic, pesticides are very dangerous for birds.
Baths. Even if they have small baths available all the time, an extra special big bath can be awesome. A wide shallow pan of water with some greens in it for the finches, and a dust/sand bath for the quail. For the water bath, birds love dripping water, so you can set up a drip from the top of the cage into a shallow pan. You can make your own from a milk/water jug and a stick (or golf tee) or buy the drippers made for reptiles like chameleons. (Finches sometimes like dust baths too!)
For the quail, since they are ground foraging birds, offer different textures in the bottom of the enclosure, like some tiles (textured and not slippery), clean rocks, a brick, and some digging boxes. Even finches spend some time down there, so they might like them too. Dried magnolia leaves can be piled in the bottom for them to dig through. You can buy them from terrarium/vivarium stores online. Bake or boil them when you get them (I love boiling them, it smells so good), and then pile some in a corner.
Probably a given, I’m guessing you’ve already offered it but just in the interest of being thorough, but for the finches, a variety of perch sizes and types, and swings.
Toys. They don’t play with them the same way that parrots do, but they find them interesting to peck and perch on. Avoid mirrors, but they do like vaguely shiny surfaces and some like bells or other things that make noise. Make sure any metal parts are stainless steel, there are no clips that could catch toes or beaks (quick links are a safer way to hang them), and no jingle bells.
Light. Put a full spectrum light (there are ones made for birds that attach to the cage or on stands to hang over the cage, though you can just use a quality bulb in even a shop light fixture as long as your birds can’t access it) over one section of the enclosure, on a timer. Birds seem to benefit from UVB, and the day/night cycle is beneficial. They should be able to choose whether to sit under the light or not.
Be careful with fabric, as birds can catch toenails in it. A good choice is polar fleece, as it doesn’t get loose threads and seems more resistant to catching toenails. Avoid cotton rope perches and toys for any unsupervised time. Sisal and manila perches are less dangerous in terms of rope, as the fibers are very short and don’t tangle in the same way as long, thin cotton.
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