What happens, I guess, is that the system partition is nearly full, while the home has a lot of free space, classic
As far as I know, gparted is unable to handle LVM. Yeah, it can see the LVM partiton, but it can’t manage the content.
If you want a GUI, you can try blivet-gui, but as far as I can see, it is unable to resize mounted volumes (you should boot with a live system). Actually, LVM volumes could be resized even if they are mounted, but you have to use the command line (commands like lvresize, resize2fs, etc.).
Note that Ext4 supports only offline shrinking, and XFS does not support shrinking.
So, you need to either log out, unmount /home and perform the resizing from CLI, or boot from another drive, e.g. Live media.
Also, I recommend to use lvresize --resizefs instead of separate volume and file system resizing to minimize potential issues which may lead to data loss.