Does the Apple Airport Utility need to be upgraded periodically?

Perhaps, but since AirPort Utility is part of the Mac operating system, the only way that it can be updated is with an operating system update for your Mac.

In other words, if your Mac's operating system is up to date, AirPort Utility is up to date.

Since Apple discontinued the AirPorts more than 4 years ago, there has not been any change or improvement in the features or performance of the AirPorts, so we've been stuck at AirPort Utility version 6.3.9 for a long time.

Interestingly, since Apple has provided basically the same version of the AirPort Utility since macOS Mojave (which came out in 2018, the same year Apple abandoned the AirPort base stations,) I would say "no."

You got here from a Related Article discussing an iOS/iPadOS privacy setting.

That particular setting will work transparently with AirPort Extreme and AirPort Time Capsule Wi-Fi gear, and with most other not-MAC-tracking gear, whether enabled or disabled. It will also work with gear performing MAC authentication, not that such is particularly recommended these days.

AirPort gear also offers the oldest of the three supported Wi-Fi security settings, so those security requirements will continue to permit AirPort gear until and unless Apple ages off the WPA2 AES setting.

The newest of the AirPort gear provides Wi-Fi 5, and lacks Wi-Fi 6 support. We’re all in the usual migration to Wi-Fi 6 as the older Wi-Fi gear ages out, too. Including aging out the newest of the AirPort Extreme, AirPort Time Capsule, and yet older AirPort gear.

AirPort Utility? No. That isn’t getting any enhancement work, there aren’t any new AirPort devices, and any changes to the app will probably be limited to bug-fixes until the app itself gets deprecated.