Should I use Sidecar with my MacBook Air as a permanent second display for my Mac mini?

No, don’t rely on it as a permanent setup. Sidecar has caveats—both Macs need the same Apple ID, network, and recent macOS, and an older Intel Air might not work with an M-series Mac mini. Even when it works, latency is noticeable for dragging windows or video, and you can’t use the laptop while it’s a display. For occasional use it’s fine, but for daily use, buy a $150 24-inch monitor instead—it’s faster, simpler, and frees your MacBook Air for portable use.