Under System profiler, is it the model iMac17,1? With the latest Monterey you can use it to restore the Mini. Recommend installation onto an external SSD or 32GB+ USB thumbdrive, otherwise you might wipe out Windows. Restore will work without an account.
(If it's an older model than 17,1 you can install Monterey with Opencore Legacy Patcher, it's more involved and I am not entirely sure if the restore will work, but it might.)
You will need a USB-C to USB-A adapter cable. The correct USB-C port on the Mini is the one on the back that is closest to the power button.
The hardware will be fine, in the future never manually delete the internal disk with disk utility on newer Macs.
For what you want to do, erasing the entire MacOS, there is a specific recommended way: Make sure Filevault is enabled, reboot to recovery, when asked for a password do not enter the password, in the menubar click on the File menu and select the "Erase Mac" option. That will format the entire storage but without wiping firmware and bricking the Mac and it will create a new fresh install volume "Macintosh HD" (sometimes called "Untitled" instead, you can rename it).
(You might need to click on forgot password and wait for the password recovery screen to show before you have the "Erase Mac" option in the File menu.)