The part that is deprecated is Apple File Protocol (AFP) -- not to be confused with DISK formats: Apple File System (APFS) or older MacOS Extended aka Hierarchical File System Extended (HFS+).
Apple File Protocol (AFP) is a Server protocol that Apple has been trying to retire for a long time. Server Message Block (SMB) has proved more suitable, and SMB has taken its place for Server traffic.
What keeps working:
• use of the Time Capsule as a Router remains, but the limited protocols and Wi-Fi capabilities it supports are getting really old. It might be a good time to consider the more advanced capabilities of a more modern Router as your Main Router, and turn the Time capsule into a repeater/extender by turning off its ability to dispense local IP addresses using DHCP. Apple calls this 'Bridge mode' but that terminology is far from standard.
• the drive that contains your accumulated backups is likely fine, and could be moved, unchanged, to an external USB enclosure and connected:
-- to ONE Mac on your network, for locally-attached backup.
-- to a different Mac on your network, running 10.13 High Sierra or higher, to use as a Shared Time Machine destination. [10.13 is the oldest MacOS that supported the ability to properly specify where the shared backup destination was located and what access was allowed by which Macs) on your network.]
It is also possible, but not guaranteed to work:
-- to the USB port of a Router that supports Time Machine features, elaborated below.
-- to a Network Attached Storage (NAS) device, elaborated below
But again, this might be a good time to ADD and additional Time Machine drive, as step toward modernizing your backups for future needs. When you ADD a Time Machine destination drive, its starts a new stand-alone backup staring with today. Every-other backup goes to every-other drive until you decide to remove one. This means at no time are you left 'working without a net'.
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Upgrades to consider:
You can also move that drive or a different drive and connect it to:
• the USB port on a modern Router -OR-
• a Network Attached Storage (NAS) device, which tends to be a simple, network-attached computer with good I/O capabilities, typically running Linux.
... PROVIDED that Router or NAS (which I am calling the Host system) supports the ability to create and maintain a 'sparse bundle disk image file'. That is an entire Virtual Disk inside an expandable file on the Host system. Using a 'sparse bundle disk image file' launders out the details of exactly how that Host system stores its files.
A 'sparse bundle disk image file' is exactly what you will see at top-level on the Time capsule drive if you were to go and inspect it manually. Keep in mind to look inside that Virtual Drive, it takes several Minutes to Mount that disk image file to use it.