After installing grapesjs-style-bg plugin, how do I add it to StyleManager?

You can cheat from here: https://github.com/artf/grapesjs/blob/gh-pages/demo.html#L1127

You must add background-bg to the buildProps array and then config it in properties, the type must be bg:

[
    ...
    {
        name: 'Decorations',
        open: false,
        buildProps: ['opacity', 'border-radius', 'border', 'box-shadow', 'background-bg'],
        properties: [
            ...
            {
                id: 'background-bg',
                property: 'background',
                type: 'bg',
            }
        ]
        ...
    }
]