If you don't have a good backup on external media, you will need to take the back of the monitor off and pull the hard drive. Then put the drive into a different computer or use an external drive case, a USB drive adapter or hard drive dock to copy the files off the drive. (You'll probably need a SATA port adapter or 2.5" drive case. The case will turn the internal drive into an external drive.) Many computer repair sites will have this equipment available and will do the entire job for a fee. (I've only done this with Windows computer systems as the recovery system.)
HP product support may have a service manual for your all-in-one. Google the model number. If you see a link to the HP specifications page, follow the link. Near the top of the page, look the the product home link. On that page, click on Manuals link on the left side of the page. For example, the service manual for the HP 19-2113w is available on the manuals page: https://support.hp.com/us-en/product/hp-19-2100-all-in-one-desktop-pc-series/6879095/model/7096373/manuals
. The direct link to this service manual is currently http://h10032.www1.hp.com/ctg/Manual/c04716104
To access the inside of the HP 19-2113W, turn off the system and unplug all of the peripherals and power cord. Set the monitor face down on a soft cloth (to minimize scratches). Remove two screws from the bottom of the monitor. Then pry up the back of the monitor/computer across the bottom of the monitor. Lift the cover out of the way. Make sure that you use safe electrical procedures and ground yourself relative to the computer as you work. Remove the one screw of the left side of the hard drive cage that holds the drive in the system. Slide the cage to the left and lift it out. (If using a USB drive adapter, you may be able to attach the dongle without removing the drive from the cage.) For all other methods of reading the drive, you will need to remove the four screws (two on each side) that secure the drive to the cage. Then slide the drive out of the cage and retrieve the data using any computer.
Note: when you connect the drive to a computer, if you do not see a drive letter assigned or get a "disk must be initialized" message, the drive has lost critical information and can't be directly copied. In that case, you will need recovery software to see if any files can be retrieved. (Recuva, https://www.ccleaner.com/recuva
, has a nice free version that can get you started. There are other programs as well. Some will not recovery anything until you upgrade from the free version.)
I hope this helps.
(The computer and hard drive manufacturers do not routinely include data recovery with a warranty repair. If your all-in-one is under warranty, do not open the case.)