I would like to have suggestions to replace the device for both of these utility: network storage and wired network extender.
Apple was the only supplier to offer a "one-piece solution".......a router with a built in hard drive, so there are no direct "one-piece" replacements for your requirements for both network storage and wired access point in one single product.
The closest that you will come would be a "two-piece solution"........ the Synology router or one of the upper end Asus routers that include a USB 3.0 port that supports Time Machine backups and network storage to a separate attached USB drive. There might be other routers that also support Time Machine backups in this manner, but I am not aware of them.
To act as an access point, the Synology router or one of the Asus routers would need to be configured to operate in Bridge Mode and the set up to provide a WiFi network that uses the exact same wireless network name and password as the current "main" WiFi router on your network.
The USB drive would need to be formatted in Mac OS Extended (Journaled)......also known an HFS+..... to work with Time Machine on the Synology router or one of the Asus routers.
Another option would be to consider a Network Attached Storage (NAS) device that would connect to your "main" router using an Ethernet connection, but Macs could back up to the NAS over the WiFi network. You will of course need to add another router to function as an access point to provide extended WiFi coverage. The Synology NAS products are popular devices with Mac users who want to use Time Machine to back up their Macs.