I have an iPhone 13 Pro Max that won’t turn on, even after I’ve tried all the troubleshooting steps I could manage on my own. Most importantly, I do not want my phone to be wiped, as I haven’t backed up important photos and videos of my cat, who passed away last February. The phone’s manual states that erasing all data is a standard procedure.

I wouldn’t resort to a factory reset without first exploring other repair options. It’s better to find a specialist who can diagnose the issue without erasing the data on your device.
Just be sure to tell the technician right away that preserving your existing information is your top priority.

When dealing with an official service centre they will often recommend replacing the motherboard or carrying out a factory reset, both options will instantly wipe all data. In your case it's best to seek help from phone repairs manchester who will be able to identify what components are at fault without wiping the data from the memory chip. A professional motherboard repair should get your device working again so that you can make a copy of your data.