HomeAssistant and OpenHAB are good places to start. I don’t know too much about OpenHAB, but for HomeAssistant you can do almost everything locally.

ESPHome is a good example of a project that they fund where you can use ESP8266/ESP32 devices to create several sensors and other devices for local IoT. They also have a number of ways to bypass cloud requirements for Tuya based devices, Phillips Hue, etc.

Plus this year is “Year of the Voice Assistant” and they’re working on enhancing a locally accessible and hosted voice assistant that doesn’t require cloud access.

Since I am on the same journey as OP and tried it just recently, I have one thing to add about openHAB:

It does not come with actual login credential handling. If you want to make your smart home accessible from outside your home network I cannot recommend openHAB.

I am currently going with Home Aisstant mainly for that reason.

If you want to make your smart home accessible from outside your home network I cannot recommend openHAB.

You can use a VPN instead for this. Which is a good idea in general, in my view, unless you need your resources to be publicly accessible.

Although I agree that even LAN services should ideally have some sort of credentials anyway.

Using a VPN does work for restricting outside access, however I found that for me this was not convenient enough for two reasons: