Zigbee does work with a generic controller on Home Assistant and other platforms, and there are >3100 devices that are compatible with zigbee2mqtt, a Zigbee to MQTT bridge that exists to bypass the need for proprietary Zigbee bridges. No proprietary app or Internet access required either, but it was not easy to set up. Here's a list of supported devices: https://www.zigbee2mqtt.io/supported-devices/

The list of Tasmota devices is extremely limited if you don't want to flash it yourself, but a bit less so if you use Tuya Convert which is done via WiFi. It seems the device list is getting shorter all the time as vendors switch to other hardware implementations, but I seem to remember reading that a new Tasmota version will be coming that supports additional hardware.

To get plug-in dimmer and smart button functionality (Shelly Button 1 didn't exist at the time) I had to put in Z-Wave. and I've since added a few new devices. Z-wave works pretty well, but not flawlessly. My Tasmota stuff just works and works much better than the original firmware on my smart bulbs and plugs.

Just getting my feet wet with Zigbee because I need yet another dimmer plug for a different location, but my understanding is most (but not all) Zigbee devices are not proprietary and work with most controllers. I'll know next week.