time machines used for back ups and AFP phase out

In addition to Bob's comments, a little background may prove useful ...

As far as Time Machine (TM) backups to a Time Capsule (TC), there are basically three things in play:

1. The format of the Mac's internal drive that will be the source for the TM backups. Prior to macOS Big Sur, the format was HFS+. For Big Sur to Tahoe (currently the very latest), it is APFS.
2. The format of the TC's internal drive. This drive is always formatted in HFS+ which is required by TM.
3. The network file sharing protocol being used. AFP = Apple File Protocol, and SMB are the most commonly used. Apple will be phasing out AFP; most likely, in the next release of macOS.

When a Mac running Big Sur or later makes a TM backup to a TC, it still creates an HFS+ sparsebundle disk image on the TC. Inside that sparsebundle, the backup volume itself is HFS+, not APFS — even though the source Mac’s internal drive is APFS. The Mac performs the translation automatically, meaning your APFS-based system is backed up to an HFS+ Time Machine volume. However, because of this, you don’t get the efficiency and speed benefits of the new APFS-based TM format introduced with Big Sur (which requires a directly attached APFS drive as opposed to the networked TC).

So, the TC still works, but it’s treated as a “legacy” network destination. The main trade-off is slower incremental backups and less efficient space usage. If you’re running macOS Big Sur or newer, Apple’s TM prefers SMB over AFP, but the Time Capsule’s older firmware doesn’t handle SMB-based Time Machine backups properly, which is why AFP remains necessary in that setup.

Going forward, hopefully you can see that this is not a simple matter of just "re-imaging" the TC's drive. It would require, most likely, a new system board on the TC as well ... and, since Apple has gotten out of the network hardware business back in 2018, there's little chance that they would get back in with an updated TC.

What I do not understand is why Apple decided to phase out this AFP language/protocol that effectively stops the use of this accessory.

Well, Apple did not "phase out" what you are asking about. Time Machine backups to a Time Capsule work just fine with Tahoe and earlier operating systems. You can verify this by reviewing the Apple Support document linked below:

Backup disks you can use with Time Machine - Apple Support

Now, if you are asking about another future operating system, our crystal ball is not good enough for that.

I am using a new mac mini with Sequoia 15.7.1 and it still works, but I am getting the warning that it's about to stop. That's what caused this post.

Nothing is about to stop; not on its own, not until a future macOS version is released, which has not yet occurred, and since you are still using Sequoia it suggests you are not one to upgrade macOS the moment every new version gets released. Nothing wrong with that.

Sequoia will continue to work with the Time Capsule. Forever. So will Tahoe. Forever. Until the hardware fails, as everything does, eventually. And all TC hardware is at least seven years old. That's old.

You are concerning yourself about a macOS version yet to be released.

There is a lot of confusion being thrown about, and Apple hasn't helped. How best replace Time Capsule backup servers? - Apple Community should help clear up that confusion.

callawaykj wrote:

What I do not understand is why Apple decided to phase out this AFP language/protocol that effectively stops the use of this accessory.

That decision harkens back to Snow Leopard means no more Appletalk - Apple Community. AFP is analogous to it. We managed.

AppleTalk was literally last century; dating back to the original Macintosh. This is just more of the same.

What we need is someone to make a youtube video that shows a step by step way to update the old TC to function with the new macOS.

The new OS is Tahoe. We already explained that an "old" TC will work with the Tahoe operating system. If something is going to stop, it is still so far into the future that no details exist.

The most recent Time Capsule and other AirPorts were discontinued more than 7 years ago. That is a long long time in the electronic world. Frankly, it is amazing that they are still compatible with the most recent OS.