What is the best SMB-capable replacement for my retiring Airport Extreme for wireless Time Machine backup?

Since Apple got out of the network hardware business back in 2018, a lot of folks found themselves having to find a replacement for the AirPort Extremes or Time Capsules for Time Machine backups.

However, there are a number of options still available, from least to most expensive, and they are:

1. A directly connected external drive to your Mac.
2. A networked Raspberry Pi, with a directly attached USB drive.
3. A router that supports connecting a USB drive. I suggest looking at either ASUS or Synology routers for this.
4. A dedicated NAS that supports Time Machine backups, like those from Synology.

Only option #1 does not require a full operating system. Option #2 can run a simple "headless" OS. Options #3 & #4, of course, will have a full OS that is accessed via a web browser.

FWIW, I currently use options #1, #2, & #4 for Time Machine, and have done so successfully for years ... including currently with my Macs running macOS Golden Gate.

see also MrHoffman User tip for additional information,

Time Machine and Time Capsule replacement - Apple Community

including this NAS:

"a Mac running macOS 11 or later and with sufficient local storage"

… Seems like a missed opportunity to instantly add value for consumers at basically no cost to Apple.

If it were no cost to Apple they could simply have added SMB to the TC. After all it's only software.

But software isn't free. Far from it. Even then, it requires ongoing legacy costs... forever, or as long as they want to support their products, whichever comes first. Apple supported the TC for as long as any of their products, and it's over.

Who knows why Apple abandoned the router market. We could speculate, but that would be pointless and construe misuse of this site.