You cannot add style to an SVG <g>
element. Its only purpose is to group children. That means, too, that style attributes you give to it are given down to its children, so a fill="green"
on the <g>
means an automatic fill="green"
on its child <rect>
(as long as it has no own fill
specification).
Your only option is to add a new <rect>
to the SVG and place it accordingly to match the <g>
children's dimensions.