You’ll just want to connect a NAS to your router (I highly recommend Synology). If you’re pretty good at navigating operating systems, you’ll be fine with Synology. Just go into the file sharing settings, then enable SMB or FTP (whichever you prefer, FTP is faster, but SMB is more likely to be supported across platforms). Then on your client device, enter the IP address of the Synology (you’ll see this on the Synology dashboard) along with the username/password that you set and you’ll be in! As long as you have a decent router with low interference from neighbors, your media should play wirelessly without buffering.
The Apple TV wouldn’t benefit from any further 802.11 upgrades. WiFi 6 is already too fast for what the device is for… streaming. Media streaming averages are 5-15Mbps for your typical apps (Netflix, Hulu, etc). TV+ streams higher than all other providers… around 25-35Mbps. That being said, the Ookla Speedtest app on my Apple TV shows I get nearly 500Mbps over WiFi. So I literally always have a minimum of 400Mbps to spare… upgrading to WiFi 6e, 7, or hell, 10 will yield absolutely no performance benefits for a streaming device.
For anyone who does experience buffering on their Apple TV… buy a decent router and don’t set it up in the closet on the opposite side of the house.