First - Be sure you have updated the software on your new iPhone - this is important if you had upgraded to the new home architecture because any devices not running the latest OS can’t use the Home App. Upgrade all software on other devices, particularly the device you’re using as a Hub. Is this Apple TV or HomePod? The new architecture (if upgraded) no longer supports iPads as Hubs. Make sure your Hub is using the same Apple ID. Same home wifi on all devices as well.
Everything in Homekit should transfer over to any other Home App supported device signed in with the same Apple ID. On your new iPhone in settings - your name - iCloud - Apps using iCloud - “Show All” and enable Home.
You can also enable the bridge by installing the Hue App on your new phone. Once you open the App you will be prompted to connect the Bridge by pressing the button on top. You will at least be able to use the Hue App to control your lights.
See if any of this helps.