How do I stop a square graphic from looking like a sticker stuck on the shirt?

Use Frames. Open the Frames tab in the Effects Studio, pick an edge texture (or one of the Dot Fade / Torn Edge presets), and the hard outer edge of your artwork dissolves so it blends into the garment instead of reading as a pasted rectangle. It works on any hard-edged graphic — photos, screenshots, AI art, anything with a straight border — and you do not have to paint it by hand or knock out a solid background colour first.