Exporting passwords
The application you are seeing is "Seahorse", which manages the gnome keyring. Its distributor's website tells us:
File Locations Gnome Keyring looks for passwords and encryption keys in the following locations:
~/.gnome2/keyrings
: Password keyrings, keys and certificates.
The export option is only available for certificates, not for passwords.
To sum it up: Backup ~/.gnome2/keyrings
, and you have your passwords.
In new versions of GNOME 3, the file is saved in ~/.local/keyrings
or ~/.local/share/keyrings
.
As of the date of this post, I'm using GNOME 3.28.2, and this is located in ~/.local/share/keyrings