I was going to mention that too , I was running octoprint on a pi model B for ages, it worked just fine unless you wanted to view the gcode progress then it would take forever to load if it was a large print (probable more a memory issue I suspect)
But back to OP - a pi zero should work ok if it only has homebridge on it.
I use the Ring and have the doorbell trigger an old Aeotec Siren.. The way I do it is use a product called Node-RED + a node (a plugin) which can trap Homebridge device events. I then have Node-RED activate the siren. All my rules are in NR rather than HE - for me I prefer the interface, flexibility and reduced hub overhead it gives me..
And this is my Node-RED "sequence". The "Front Door" node (orange box) waits for an event from Homebridge and when it triggers sends a message (object) down the wire to the next node, in this case a time-range node which won't let anything pass unless it's in a given time frame, if okay then the message travels to the "Living Room Door Chime" HE Command node (green box) which plays sound # 4 on my Aeotec Device (which is paired to HE). Works great!
Edit: I know this sounds complicated but it really isn't. Companion servers such as Node-RED and Homebridge augment the power of HE and provide additional flexibility and control. It is NOT for everyone though so ymmv.
Correct, you need the pro bridge 2. The one you're looking at doesn't support telnet which is how HE communicates with lutron. Liuke I said, Lutron just works (I have around 45 dimmers and switches and pico's). Lutron does have an on/off switch in their caseta line but that does require a neutral. Innovelli has one that does not. If you want to control smart bulbs with a smart switch use Innovelli as they can have the smart disabled so they don't interfere. If you can though I would return all those bulbs and start over.