How to have the "Restore Missing Files" function from Nautilus without installing Nautilus?

The codesearch says that it is Deja Dup Nautilus extension.

It has its code on LaunchPad and deja-dup is called from NautilusExtension.c file:

cmd = g_strdup_printf("deja-dup --restore-missing \"%s\"",
                   nautilus_file_info_get_uri(info));

g_spawn_command_line_async(cmd, NULL);

It is also known that Caja has integration with Deja Dup too via deja-dup-caja package.
So you can use Caja with this extension.

Theoretically we can try to write our extension with FileManager Actions or something similar to have this in context menu.

The complete method is the following - we need to create user-action file and place it in special folder (the method is based on this answer) :

mkdir -p ~/.local/share/file-manager/actions
cat > ~/.local/share/file-manager/actions/deja.desktop << EOF

[Desktop Entry]
Type=Action
Tooltip=Restore Missing Files
Name=Restore Missing Files
Profiles=profile-zero;
Icon=deja-dup

[X-Action-Profile profile-zero]
MimeTypes=inode/directory;
Exec=deja-dup --restore-missing %u
Name=Default profile
EOF

and use it:

Once again --- posting the question led me to find the answer.

When I edited the question and wrote "Perhaps it's a command that Nautilus sends to deja-dup" .... sure enough,

deja-dup --restore-missing DIRECTORY

Farewell Nautilus!