Peter,
Thanks for posting your specs and to David for the fast reply on compatibility.
If you want to continue to use the latest OS X OS for current software (recommended for speed, security, features and compatibility with modern software), then you can set up your new Mini to dual-boot so that you can boot into an earlier version of the OS to run AC 11... or create a Virtual Machine that runs an earlier version of OS X and AC 11. If you want SSD speed for AC, either of these would require that your new SSD be large enough to be partitioned into two boot volumes. You can store all of your files on your main current OS X boot volume so that they are backed up by Time Machine and available to all of your other apps when running 10.9.3 or newer.
Rebooting will be a hassle; running a Virtual Machine will offer AC less system resources and hence slower performance.
Of course, the cleanest solution is to upgrade to AC 17/18 - but that'll be pricey jumping from 11. And... the mini's onboard graphics adapter is not recommended for recent versions of AC which perform best with dedicated graphics cards. On-board cards such as the Intel in your mini are below the required specs:
http://www.graphisoft.com/support/system_requirements/AC18/index.html
Yet, for AC 17, the graphics card page does note (as have other users here) that the Intel 4000 that you have can work:
For the best performance choose Mac computers with dedicated graphics cards. Integrated Intel HD 3000, 4000 cards work with ArchiCAD, but their performance is limited.
Since you were running 10.6.8 before... I have to wonder if you also have some old PPC programs that require Rosetta - not available after 10.6.8 - to emulate PPC and allow them to run. For example, AC 9 and earlier can run on 10.6.8 but cannot run in more recent versions of OS X.
One of the forum moderators
AC 28 USA and earlier • macOS Sequoia 15.2, MacBook Pro M2 Max 12CPU/30GPU cores, 32GB