-1-You could use WOL to wake the desktop computer so the shared folder would be available. Free but when you send the Wake on lan command it can take sometime before the drive is available.
-2-You could use a NAS, either a standalone NAS or if the router has a NAS feature and can use a usb hard drive to behave like a NAS. I know that some Asus routers have that (or it's a feature of Merlin, that I was using on an Asus router), there is also freenas that you can use on an old pc that you would keep always on. Performances of nas feature of a router are typically on the low end. Also keep in mind that if you store valuable files there, you need to have a plan in case the hard drive goes bad.
-3-You could store the files outside your house like One Drive or google drive and access it from both computers.Access from local device should be faster but with sonic fiber, you may not see the difference unless you store gigabyte size files.
-4-You could use something like syncthings to synchronize a folder on both computers.the data is replicated on both devices.
My personal solution is to have a computer always on with a bunch of hard drives pooled using stablebit drive pool so if one drive goes bad, the data is still available.Additionally, i have a pool above that comprised of the other pool of drives and a storage at azure (using stablebit cloud drive) so that if the house burns in flame, the data is still safe at azure (it can also work with other cloud providers)
Depending on your needs if the router you use does have a nas feature and can use a usb hard drive it can work.
Otherwise you can get an old pc or a purpose built NAS (like synology, WD "my cloud" or something else) put one or multiple disks in it and plug it to one of the network ports on your router.
Good luck. it's an interesting project to work on while sheltering in place.