You’ll also need to add “svg” to the list of valid extensions in WP_Customize_Image_Control
:
$wp_customize->add_control(
new WP_Customize_Image_Control(
$wp_customize,
'themeslug_logo',
array(
'label' => __( 'Logo', 'themeslug' ),
'section' => 'themeslug_logo_section',
'settings' => 'themeslug_logo',
'extensions' => array( 'jpg', 'jpeg', 'gif', 'png', 'svg' ),
)
)
);