How to backup and iPhone XR with an unresponsive touch screen? Or fix the problem?

Hello! Does anyone know of a way to backup files on an iPhone XR that has an unresponsive touch screen? I do not have access to siri or anything like that now because I had reset my iPhone several times to try and fix it, so now i need to enter my passcode if i want to talk to her, and i can't do that bc my screen is unresponsive to touch.

All the buttons work and the phone itself (apart from the touch) seems to work fine–I can see i'm getting notifications, etc. But I just can't use it at all. It was totally normal until the other night when the screen just stopped responding to my touch. in the past there would be a small portion of the screen that would have problems like this on and off, so I'm sure the problem could be related to that which would likely mean it's a hardware not a software problem, right? For reference, there are a few cracks in my screen. I could have maybe touched my phone when my hands were a little wet after washing them, and maybe that did it in? I had a (cracked) screen protector on at the time which i since took off to see if that would help.

Does anyone have any experience with this, and know of a way to fix it (I understand, likely not). My last resort is doing the full restore through iTunes (which i know wouldn't help if this is a hardware issue), however, i have many pictures I would really not like to let go of if i can help it, and I'm pretty sure my iPhone hasn't been backed up for a long time. my iCloud storage is full, and my laptop is pretty full/old lol. Can i back it up without tapping "give permission" on my iPhone?

I can't go to an apple store because I am in a rural area in a foreign country. I just genuinely don't know what to do!

Any advice would be greatly appreciated:)