I’m using a ConBee II in this configuration without much issue. There are a couple of things you can try:
Make sure the ConBee is on a USB extension cable and moved a bit away from the computer case rather than just plugged right into a port on the back.
Are you sure the stick is close enough to one or more of the bulbs to communicate reliably? Zigbee has pretty good range, but environmental factors can make a big difference. You could try an experiment where you put one of the bulbs into a lamp you could move around to test signal reliability.
In the ZHA integration configuration it is possible to change the Zigbee channel. Tap the pencil icon next to the channel (NOT “Migrate Radio”). There is a warning about channel migration being experimental but if all you have is Hue bulbs I wouldn’t worry too much (my bulbs are Tradfris, and they were fine at least). I had to do this initially to get reliable coverage, and everything has been solid since.