Configuring the Logitech MX Vertical

Install xbindkeys and playerctl: apt install xbindkeys playerctl

Run xev | grep button to find out the key codes. Press the buttons to reconfigure and note the values in the console.
The forward and backward buttons have the following values:

state 0x10, button 9, same_screen YES
state 0x10, button 9, same_screen YES

state 0x10, button 8, same_screen YES
state 0x10, button 8, same_screen YES

Start with the default config file: xbindkeys --defaults > ~/.xbindkeysrc

Add the following lines to that file:

# Toggle media playback with the Logi mouse *backward* button
"playerctl play-pause"
    b:8

# Skip a track with the Logi mouse *forward* button
"playerctl next"
    b:9

Use xbindkeys --poll-rc to reload the config.