That's what my house does. If I kill the internet, automations still work, as well as the interface via LAN (I've got hairpin NAT set up to make this easier than having 2 addresses in the app), if I kill Home Assistant, all devices still function manually.
I favor ZigBee to WiFi smart devices, although the polluted spectrum in my area gives me some headaches. With WiFi devices when possible I buy premade stuff (so that it's CE compliant), and flash ESPHome on them, or similar.

[–] jj4211@lemmy.world 1 points 8 hours ago

Yeah, wifi is a crapshoot as to whether it might expect a cloud connection, so I have to research those devices carefully. I'm satisfied with my OpenGarage being on Wifi because I know it has no internet aspirations. I hope that Matter over Wifi devices are similarly local friendly, but I haven't actually had anything to buy since that was an option.