Connect a USB mouse to the phone via an OTG cable and use the mouse to navigate through the phone so that you can backup your data to the cloud. Search online for Samsung S10 OTG cable to get results for suppliers that suit you best.
Be aware that the phone’s battery is used to power the mouse so it will discharge more quickly than normal.
After that you can replace the LCD screen + digitizer as described above, to fix the touch problem.
Replacing the screen assembly doesn’t require a hard reset so if you are careful, your data shouldn’t be affected. If you backup your data first nothing untoward will happen to it because of the repair, but odds are if you don’t then it will. Murphy’s Law.