Mac mini with an iPad as the only display?
Sidecar lets you use an iPad as a secondary display for your Mac. So Sidecar doesn't have any such kind of mode that lets you use an iPad as the only display.
You can, however, explore some 3rd party solutions which claim to make your iPad usable as a standalone display for a Mac mini. A such prominent 3rd party solution is Luna Display, Headless Mode

https://shop.astropad.com/pages/headless-mode


With Luna Display, turn your iPad into the primary display for Mac mini. Combine the best of Mac mini and iPad by harnessing the processing power of the Mac mini and the edge-to-edge full display of the iPad.
Minimum Requirements

Mac mini must be a 2011 model or later, and running macOS 10.11 (El Capitan) or later
iPad must be an iPad 2, iPad Mini, iPad Pro, or iPad Air model running iOS 9.1 or later (32-bit devices are not supported)
External mouse and keyboard connected to Mac mini are optimal for this setup in case of MacOS permissions and logins

How to Get Started

An external display is required to get set up, but is only needed the first time you configure your devices (unless FileVault is enabled).
Luna Display requires a Mac application to run. For Headless Mode, if FileVault is in use, an external display will be needed to unlock your drive whenever you reboot.



https://help.astropad.com/article/218-how-do-i-use-luna-display-in-headless-mode



Headless Mode: Using your iPad as the display for Mac mini
What you will need to get started:

Mac Mini

iPad

Luna Display and latest versions of the Luna Display apps, available for download at lunadisplay.com/hello


Reliable local WiFi network connection or USB cable
We recommend connecting an external keyboard to your Mac mini.


P.S.: No affiliation whatsoever with Luna Display or any subsidiaries. Never used it personally before.