Hi Pascal
A few points:
1. The first thing I notice is that the memory card appears as "/dev/sda"  in your df command on the DL device.
This is what you should see in the /dev directory:
root@Digital-Library:~# ls -l /dev/sd*
brw-------    1 root     root        8,   0 Jan  1  1970 /dev/sda
brw-------    1 root     root        8,   1 Jan  1  1970 /dev/sda1
"/dev/sda1" is the first partition on the "/dev/sda" memory device
The library memory should appear as "/dev/sda1". It will then be mounted as "/mnt/sda1"
This is the df command output on a working DL system:
root@Digital-Library:~# df
Filesystem           1K-blocks      Used Available Use% Mounted on
/dev/root                 3840      3840         0 100% /rom
tmpfs                    62432        84     62348   0% /tmp
/dev/mtdblock6           10816       456     10360   4% /overlay
overlayfs:/overlay       10816       456     10360   4% /
tmpfs                      512         0       512   0% /dev
/dev/sda1             61387804  56862020   1407448  98% /mnt/sda1
I suspect that something has gone astray in the formatting / partitioning of your card. 
You should have a single ext2 formatted partition on the card.
 
I usually use the GParted graphical utility on Ubuntu to format SD cards and USB sticks. Just use the ext2 selection to format.
Perhaps you could try this out on a smaller USB memory stick just to get things sorted out before attempting it on the 64GB SD card.
2. The contents in the top level of the SD card don't look quite correct.
This is what a working card looks like:
 --------------------------
root@Digital-Library:~# cd /mnt/sda1
root@Digital-Library:/mnt/sda1# ls -l
-rw-rw-rw-    1 1000     1000             0 Jan  1  2014 ##LIBRARY##
drwxrwxrwx    2 1000     1000          4096 Nov 16  2020 art
-rw-rw-rw-    1 1000     1000          1367 Jun 15  2014 common.css
drwxrwxrwx    2 1000     1000          4096 Sep 15  2013 css
-rwxrwxrwx    1 1000     1000         47602 Jan 18  2021 index.html
drwxr-xr-x    2 1000     1000          4096 Nov 28  2020 local
drwxrwxrwx    2 1000     1000          4096 Jan  1  2014 logs
drwxrwxrwx   46 1000     1000          4096 Jan 17  2021 modules
-rw-rw-rw-    1 1000     1000          4354 Jan 18  2021 style.css
-----------------------------
The sizes shown for the directory entries on your card (eg art, css, local etc) are much larger than they should be (4,194,304 compared to 4096 on ext2)
Also I see a "System Volume Information" directory is present. Where has this come from??
Looks a bit MS Windows like...
This makes me wonder if the card is actually formatted as ext2 with its default 4k block size. 
It looks a bit like it might be the original exFAT format that the card would likely have had on it from the factory.
I usually use the graphical GParted utility on Ubuntu to format SD cards and USB sticks. 
Just use the ext2 selection to format.
3. The Home screen you are getting when the card is plugged into the DL device is clearly not from your "index.html" file on the SD card. )
(It is missing your extra link, and the icon for Wikipedia for Schools.)
It looks like the default screen you will get if there is no library memory card installed. You might like to check what you see with no memory installed and compare.
This confirms that the SD card in the USB adapter is not being recognised by the DL, as above. 
Again, I suggest that you experiment with a smaller USB memory device (eg 8GB)  to get the basic formatting sorted out, and the basic library files in place and working before moving on to the larger SD card.
Regards
Terry