How to unlock my old iPhone without losing the photos?

Sorry, not possible.

If you forgot the passcode on your iPhone, or your iPhone is disabled or unavailable -

Click on the link for instructions on how to reset your passcode without a computer if you have iOS 15.2 or higher.

If you see an iPhone or iPad unavailable message or Security Lockout screen - Apple Support

Click on the link for instructions on how to reset your passcode using a computer.

If you forgot your iPhone passcode - Apple Support

We have this issue with a 1st gen iPad. My wife is original and only owner, and seems like that can be verified by Apple based on serial number and AppleID.

There’s no way to unlock it?

No. There is no way to bypass a forgotten or incorrectly entered Lock Screen passcode that has resulted in the device bing disabled or unavailable.