What should I do about this big root while edging around the tree?

I’d avoid cutting a large root close to the trunk. Roots help support and supply the tree, and whether one can be pruned safely depends on the tree and the root, not on a simple size rule. Shift the curve outward or shape the edging around it. If cutting seems unavoidable, ask a qualified arborist to assess it first.

Move the edge a few inches, or make a wider curve around the root. It’s usually easier to adjust the border than to risk damaging a root you can see is substantial. You could also use an edging style that sits above the soil rather than digging deeply beside the tree.

Think about the whole area around the tree, too. Avoid piling soil or a thick layer of material over the root, and try not to compact the ground while you work. For a planted or mulched feature, a simple mulch layer can be easier to maintain than a buried weed barrier.