Inventory is through our POS/processor and production records are through Beer30 (though I have plans to write my own and open source it when I have time; we just opened and we're all still running pretty hard doing new-open stuff). We're also technically a nano-brewery, so anything we're doing is a little bespoke (i.e., I think it's a very situational setup) right now.
The biggest thing from a brewery-specific side that we're doing is controlling the brewhouse. We're running an all-electric system, and all the heating and cellar controls expose UIs over the LAN. In addition to being generally nifty, we're using Unifi to separate brewery-specific stuff onto its own network and the built-in VPN hosting (I opted for the OpenVPN option) to expose that network security. This allows our brewer to do stuff like check the temperature from home or set the boil kettle to start running before he leaves the house. (The useful thing about the UDM (primary server) running Alpine is that I have a task that essentially functions as dynamic DNS and updates an A record with our domain provider so he can always log in at a known hostname).
It also integrates with cameras, phone, and menu boards, which are all useful for the FoH side of things.
All-in-all, we're not doing that much with it yet, but it's pretty nice to use so far, and being a software engineer, I'm excited for the possibilities of useful stuff I can host on it.