Possible to use external drive APFS on Time capsule for time machine backups?

Short answer: No. The Time Capsule itself is effectively “frozen in time.” Apple discontinued it years ago, and its firmware never got updated to understand APFS. Because of that, the internal disk in the Time Capsule must remain HFS+ (Journaled), and the same goes for any external USB drive you plug into it — the Capsule just doesn’t know how to share an APFS-formatted volume over the network.

Now, there’s a workaround if you’re determined to keep the Capsule in play. You could still connect an external SSD to the USB port, but you’ll need to format that SSD as HFS+ if you want the Capsule to share it properly. Your Macs running newer macOS versions can still back up to it, but the backups will be in the older format. If you want to use APFS for Time Machine (which is required for macOS Big Sur and newer if you’re starting fresh), you’ll need to connect the APFS drive directly to the Mac via USB/Thunderbolt, or share it from another Mac or NAS that supports APFS volumes.

Would it be possible to attach an external SSD formated in APFS and use time machine on that?

The old and slow USB 2.0 port on the Time Capsule will only work with Time Machine backups on hard drives that are formatted in Mac OS Extended (Journaled), aka HFS+

That port tends to be underpowered, so some users have found that they need to use a powered USB hub when a drive is connected to the Time Capsule.

When the drive is formatted this way, it is not necessary to partition the drive for different Macs, since Time Machine creates a "sparsebundle" file to contain separate backup files for each Mac.

It's hard to remember that even the "newest" Time Capsule was designed in the 2012 timeframe......long before there were even rumors about APFS. Apple never changed or updated the hardware in the Time Capsule, although different drives were used in different versions of the Time Capsule.

Yes, you can definitely use an old Mac mini as a sort of “backup server” for multiple Macs over Wi-Fi. Essentially, you’d be turning it into a lightweight Time Machine server. The mini would host the external SSD, and your other Macs on the same Wi-Fi network could point their Time Machine backups to it. This works well if the mini is always on and connected via Ethernet (recommended for speed and reliability, since Wi-Fi backups can get slow with multiple Macs).

As for the oldest Mac mini that can handle this: any Intel Mac mini from 2014 or later will support APFS volumes without issue, since macOS High Sierra (2017) introduced APFS and those machines run it fine. If you want a really budget-friendly option, a 2012 Mac mini will technically work, but it won’t officially support the latest macOS, and APFS performance on spinning disks inside those machines is pretty sluggish. For your use case with an external SSD, I’d suggest going no older than the 2014 model, since it still runs macOS Monterey and supports APFS natively without hacks.

On formatting: stick with a single APFS volume on the SSD. TM automatically creates a sparsebundle for each Mac, so there’s no need to manually partition per Mac. This way, the drive space is shared dynamically — each backup only uses what it needs, instead of carving up fixed chunks that could waste space.