I-phone 13 frozen and dead since first week of August 2024, force restart does not work,

If the iPhone has suffered a hardware failure, as seems likely, and you didn't make a backup of your photos and data, then sorry but almost certainly they're gone. Without the phone working, there's no reliable way to get the data off of it. There are some data recovery services that claim to be able to get data from an iPhone, but their chances with a dead phone are slim and recovery, if successful, is likely to be expensive. But it's your only hope.

Regards.

Sorry, but repairs are going to erase the content of the phone, so the photos and other data are gone unless you have a backup on another device or service.

When you get the repaired phone back, my advice would be to set up backups to iCloud, so your phone will be automatically backed up each day, so you will always have a current backup of your valuable data on the phone.

Tip....users who do not back up their iPhones are going to lose all of their data at some point. The only question is "when".

Most of us learn this lesson sooner or later; that the only way to mark data as being valuable is with backups.

Too often, we learn get to learn this lesson the hard way too; with data loss or theft, dunking, whatever.

As stated above, your only possibility is somebody that is both willing and able to diagnose and repair this iPhone while also preserving the data, and attempting even a failed repair with no recovery won't be cheap. And I wouldn't expect recovery to succeed.

If iCloud Photos was not enabled, and if the data is not available by logging into iCloud.com or elsewhere, then the data is gone.