There's "smart", as defined 20 years ago...which is timers, complex schedules, etc. And, then there's "smart" as we define it today, which is WiFi, browser or app-based UI, etc. I'm unaware of a Nest competitor that is not tied to the cloud-based service of the provider. I am not super attuned to the market, however. Things have likely (hopefully) changed since last I researched things like Nest a year or two ago.
Apple HomeKit works without cloud services. It is entirely local with your phone, mac, iPad etc directly interacting with the devices. I'm sure some of the individual devices from partners may leverage cloud services but I have yet to purchase a device that requires it. The only "cloud" aspect is if you want remote access to your devices an AppleTV can act as a proxy/gateway that let's you control your device from the internet rather than the local network. The eco-system is a hot mess at the moment but the basic design is well thought out.
Yes, I have a system with browser and mobile ui, based on zwave, 433mhz and modbus devives. The software I use is symcon, which has existed for 5 years at the least; but there is also eg openhab for those insisting on open source only. I optionally have internet integration too, but strictly optional.
I have only seen ones that allow you to program them (wake, leave, return, sleep) but wifi enabled for querying I have only seen ones that require a cloud account, even if you can also locally query them.