Error 14 while updating the OS when device is on Recovery mode

My iPhone XR got full of space and started to lag, hence I rebooted the device.

The device gets stuck at apple logo and later goes to recovery mode.

When I try to update the OS through iTunes it throws an error-14 mid 40% of the update.

When I looked out for it over the web it says that the device is full of storage and hence the firmware cant be uploaded on the phone due to which your update is failing midway.

Technically, when I am trying to update the OS the OS must not eat up the space like in my case. It must replace the old OS, otherwise how will I update without loosing the data. Apple customer care says that your device must have a minimum of 5 gb while you are updating the device in recovery mode, but how will a user create that space if he is stuck at Apple logo?

II) The device failed to respond at all once all the memory was full. Does that mean that whenever my phone will be full on storage I will be loosing all my data due to this loop of getting stuck to apple logo where I cant get into my phone?

I cant Restore my phone as I don't have any backup and I can't afford to lose my precious data. I spent so much money over this phone so that I can stay relaxed about my data and all of a sudden its all gone.

I need help Apple! I have trusted you so much!

[Personal Information Edited by Moderator]