There are a few threads about this already, Here is one. I know there is at least one more as I remember posting in it, and I think a new firmware release was done. Zooz recommends you update to the latest firmware.
Yes, contacting Zooz support is the only method by which Zooz distributes firmware updates. Hubitat also doesn't have any Z-Wave device firmware updates built-in, either (Zigbee updates are downloaded from Hubitat's servers upon request from the "Update Firmware" command in supported devices; Z-Wave is done by the buillt-in app with a file you provide, or by another method of your choosing).
I don't know if anyone else is experiencing the flood of battery level messages from the Zooz Zen34 button, but it just started up again on my device. I've installed the Zen34 1.3 firmware and it didn't fix it. You can see the messages when text logging is enabled for the device.
For me, the messages come in at 6-8 second intervals, runs for several hours, then seems to stop randomly. It fills up the logs very quickly. At one point I got a hubitat warning of excessive activity.
This has happened on other battery Zooz devices when they have multiple hops on the zwave mesh or otherwise not getting a great signal. To test it, you could move it closer to the hub temporarily and see if that makes it stop?
Thanks I will try that. Unfortunately if this is the problem, I don't see how I can move the device to another location as it controls a nearby dimmer.
I wouldn't expect you to keep it there, but if that makes it stop you can go back to Zooz and tell them the 1.30 update didn't fix it and what you have found. They can hopefully figure it out faster if you give them something to go on. You could even open a ticket now and just let them know what you are going to try. Maybe they will have other suggestions.
I have this same problem with my Zen34, Zooz insists that 1.3 firmware fixed the problem, but I am convinced it does not. My Zen34 came with 1.3 firmware. Following their instructions I uninstalled it, reset it and reinstalled the firmware, all to no avail. After a few weeks it again started spamming the hub with battery messages. I also agree with jtp10181 that the greater the distance from the hub the more likely it is to happen. I hope they have a fix but until then I have uninstalled it.
I've been working with Zooz the last 2 weeks on this and Friday they sent me new firmware to test. I'm not done testing all of it yet, but so far wakeup events from the Zen34 are not producing the barrage of battery info messages anymore.