Since I don't see it mentioned here I would like to suggest z-wave (protocol) and the accompanying ecosystem as an alternative.
I have multiple lights, power plugs and sensors operating on z-wave being controlled by Home Assistant. None of these require me to log into a third party app or service.
ZigBee is the open protocol that most people should try to prefer to support open standards. But both Zwave and ZigBee are local-only, so either one is better than something that can call home on the internet.
I've noticed a lot of z-wave adopters seem to be shifting towards zigbee. I guess because it is closer to thread and matter? Some devices seem to be upgradeable for that too.
I have multiple lights, power plugs and sensors operating on z-wave being controlled by Home Assistant. None of these require me to log into a third party app or service.