Backup fails due to missing storage

I am using a Sony Xperia X. Before getting the new update, I would like to make a backup. All attemps to backup unfortunately fail.
At first, I got the error message “could not access xxx” (translated). Then I found out that the system strorage might be too small compared to the amount of free space needed (SD card is completely empty). So I deleted pretty much every Sailfish app and also manually removed all large files I could find (downloaded maps, etc.)
Now, I am left with a pretty much unusable phone, because everything is gone. Compared to the beginning, the backup process advances a bit further, but it still stops with the error message: not enough storage available.
In the storage overview, I can see that 1.3GB of system data is used and 1.1GB free. From the used space, Sailfish and other files occupy 1.1GB, Android 145MB, Sailfish Apps 26MB.
At the moment, I do not know what to do or what else to delete.
I read that I might have to enlarge the system space. Yet, I am hoping that I can do a backup before trying such things. At the moment, I do not have any backup because I deleted the old one in my attempt to make some space.
So far, I have just used Sailfish. I have never done anything involving command line inputs, etc.
Thanks for any help!

I didn’t even know you could back up to internal memory. Are you sure that is what you are doing?
At least i can only choose SD card for backup… Maybe you do indeed have access/permission problems with it.

What is hiding behind that xxx would also be good info.

Seems like you ran into this
and probably caused by this

I guess you have lots of photos/videos on device storage?
Then move (not copy) those big files to SD card or PC manually.
And try again.
Afterwards you may copy those photos/videos back to device.

Great, that helped! Thank you very much! That saved my day. I only focussed on the system storage and never realized I could also make the backup itself smaller.

@attah: maybe this was not clear. Of course I tried to backup to SD card. As far as I understood, there is still some system storage space needed in order to handle the backup.