Time Capsule will no longer work starting with macOS 27 Golden Gate. It uses a deprecated format for networking (AFP), and while that format works with macOS 26 Tahoe, the format will no longer be supported by Apple starting with macOS 27. It has been over 7 years since the Time Capsule was last sold by Apple, and that means the product is now considered 'obsolete'.
There is no longer any way to connect to a Time Capsule because the networking protocol used by the device is no longer supported by macOS. Unfortunately, than means your Time Capsule is now a sleekly-designed paperweight.
If you have access to (or can borrow) a Mac running macOS 26 Tahoe or earlier, you can connect that to your Time Capsule and copy the files off. Alternatively, to recover the data from the Time Capsule, you can remove the drive inside the device, then use an external drive enclosure to connect the drive to your Mac.
https://www.ifixit.com/Guide/Airport+Time+Capsule+A1470+Hard+Drive+Replacement/61924
In terms of the functionality provided by the Time Capsule, the simplest method to continue using Apple’s Time Machine to back up your Mac(s) is to buy an external drive and connect it to the Mac(s) regularly to back them up (or leave the drive connected to a desktop Mac). External storage is relatively inexpensive, a 1 TB SSD or a 2-4 TB HDD can be purchased for <$200 (prices have gone up significantly in recent months, unfortunately).
To back up your Macs over WiFi, the most straightforward way is to use a network attached storage (NAS) device – essentially a box for hard disks that connects to your network. Ideally, choose one that offers turnkey support for Time Machine out of the box, both Synology (setup instructions) and QNAP (setup instructions) do so. Technically, you can stand up a Time Machine server in other ways (including using a Mac as a TM server), but an NAS is arguably the most straightforward way to set up network Time Machine backups.
Personally, I use a Synology DS223j with a pair of 10 TB HDDs installed to back up 5 Macs in the house with Time Machine (separate shared folder for each Mac sized at ~2.5x the internal storage), with the remaining space used as general file storage for everyone in the house.
