I did the update, added the app and exposed one device to HomeKit and while I was able to add the bridge fine, when the device came over, the '*** controller' device shows 'No Response'. The button device doesn't show this, but then, I'm not sure it would? I've force quit the Home app and re-launched, no difference - it shows "Updating..." for a bit and then goes to "This accessory is not responding." - other 105 HomeKit accessories (some native, many through HomeBridge - subset of them through MakerAPI, and some through scrypted) are all responding fine, so I doubt this is an issue on my network.
Rebooting the HE doesn't help, either.
No logs of interest, either ... I don't see an option in the app to enable more debugging logs, but I may have missed it.
Edit: using the Discovery app to view mDNS broadcasts, I do see the Hubitat bridge (Hubitat Main, in my case) - so it appears that it is visible on the network.
hubitat-lan.local resolves (can ping from MBP) and
nmap shows the port (60000) is open as well.
Edit 2: trying to add additional info as I think of it - I have 5 eligible HomeKit hubs on the network, 3x Apple TV and 2x HomePod mini. Currently a HomePod mini is the connected hub. I mention this as I believe as of sometime in iOS 15.x all HomeKit communication to bridged devices got routed through the hub, instead of device->bridge direct. e.g. previously, my Home app would connect directly to the Lutron Caseta hub or to the Homebridge device, but since then, it has to hop the connection through whichever hub is connected, so Home app on iPhone -> HomePod mini -> Lutron Caseta.