Now it’s my turn to sound like an A.I. chatbot:
Oops! @gilby101 is right! I had forgotten that Apple dropped its version of the ntpd server as of macOS Mojave!
I don’t have any experience with chronyd, but you still have several alternatives, depending on your objective.
I forget how you configured your mini to be “LAN only,” but if you just want to sync to something on your local network, the most reliable method would be to get the time from your router, assuming that your router supports time services and your mini can communicate with the router’s LAN interface.
Many routers have built-in time servers. Depending on the model, the router’s time server (as distinct from its time client) may be configurable via the router’s admin interface…or not. For example, my ISP-provided router has an active time server, but it only exposes the time client configuration via its admin pages. Check your router’s documentation.
If your mini can communicate with the router’s LAN interface, but you don’t specifically see an admin page, you can check to see if time services are available on the router by entering sntp <router's internal IP address> on a Terminal.app command line. For example, my router’s internal IP address is 192.168.1.1, and when I enter sntp 192.168.1.1 from my Mac, I get a single-line response that looks like: -2.227976 +/- 0.023253 192.168.1.1 192.168.1.1. For most home users, the numbers don’t matter very much, just that they exist. If your router does not have active time services, you’ll either get a lengthy “Timeout” error or no response at all.
Another LAN-only solution would be to set up a local time server. You’ve mentioned before that you have a Linux system available. If the router method doesn’t work, consider using the Linux system as a time server. Time service is a very basic capability on Linux. Setup generally is pretty easy, but the specific steps will differ based on the distribution. Do some googling.
If you really are interested in having a Mac act as a time server, you can try third-party tools, as @gilby101 suggested. I also notice that Apple introduced a new macOS time server in Big Sur, but it is disabled by default and is sparsely documented. For more info, search for “sntpd on macOS”, as distinct from sntp (without the “d”). There’s also a man page (man sntpd). Unless a third-party tool offers unique functionality that is important to me, I like to see if the Apple tool works first.
Edited: fixed some typos and made some minor wording changes for clarity.