How big is your boot drive in your 2013 iMac? Do not get a Mini with less storage than what you have in your iMac.
If you buy a new Mini it will be preloaded with Tahoe 26. Some of your apps will may not be compatible with Tahoe 26.
Which software are you concerned about?
You should check with the software's developers to make sure the software you're interested in will be compatible with macOS Tahoe 26 or if they have a version that will work it the newer system.
If you decide to buy a refurbished older Mac that will run Monterey the only 3rd party source to trust is OWC (MacSales.com). Apple has refurbished units but they tend to be the newer models unable to run Monterey.
