I am unable to connect my Phillips Hue bridge to my HomeKit after updating my iPhone 15 Pro Max

I’m not sure what else to advise unless you want to factory reset the Hue Bridge and lose all your saved bulbs and scenes. This error has popped up before with some Users and Philips took the blame for it. Usually Hue will say it’s Apple, then Apple will say that it’s Hue!

The other option is to see if the issue is with one of your Apple Hubs (Apple TV, HomePod). Either of those could be factory reset and set up again. What are you using as a Hub?

With Apple TV you can use the settings - system - Reset and would need to reinstall all the Apps and sign in. Or you could just try signing out of iCloud in your account on ATV and signing back in and set up HomeKit on that again. This last method is less work to go through.

I would start by rebooting the wifi though, in case it wasn’t connecting.

Try deleting the Hue App. Reinstall from the App Store and once you open it, it should require you to press the button on the Hue Bridge to connect to the Hue App, then try connecting it to HomeKit again in the Hue App. All the data (bulbs and scenes) should be saved in the Bridge because you aren’t resetting that. See if this works.