ZigBee is a fully local mesh protocol. Matter is a local protocol that can run over either WiFi or over Thread, a local mesh protocol designed to replace ZigBee. Zigbee, Matter and Thread are your friends.
I cannot even begin to recommend this highly enough:
https://sonoff.tech/en-nl/products/sonoff-zigbee-thread-usb-dongle-dongle-plus-mg24
Get one of those - or an equivalent device from another manufacturer - to allow Home Assistant to talk directly to your bulbs using Zigbee or Thread. With that, you HA can speak directly to any bulb that uses Zigbee, Thread or Matter which is 99% of the bulbs worth bothering with.
Anything that connects to WiFi without explicitly using Matter should be avoided at all costs and especially if it uses Tuya - look for the mark of the beast hidden on the packaging of kit sold under other brands.
IKEA Tradfri (ZigBee) and Kajplats (Thread) bulbs are excellent, especially for the low price. Philips Hue (ZigBee/Thread) is the gold standard but not cheap.
Devices running ESPHome or Tasmota are rarer but also highly hackable and work entirely over local WiFi. Take a look at Local Bytes for some good kit like that.