GIMP review
The first time a cutout goes on a darker background, every rough bit of the edge shows up. GIMP gives you a layer mask you can go back and paint, so a little too much trimming around a sleeve or a strand of hair is fixable.
Start with the background you already have
Select the photo layer and open Layer → Mask → Add Layer Masks. Starting with a white mask keeps the whole photo visible. Click the mask thumbnail before painting. Black hides that part of the photo, white brings it back and grey makes it partly transparent. For a portrait with wispy hair, I’d hide the big areas first and spend the extra time at the edge of the silhouette.
Put the cutout on the colour you’ll publish it on
Put a flat colour layer below the portrait and look for a halo where the old background showed through. Try a second colour if the portrait has to work in both light and dark layouts. Disable Layer Masks lets you check the original photo without deleting the mask. Save an XCF copy so you can revisit the edge later. If the cutout is going into a page design, Penpot gives you a place to check how that image sits with the rest of the layout.
Wilber artwork by Aryeom Han, used unchanged under CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/). The original is at https://www.gimp.org/about/linking.html#wilber-the-gimp-mascot.
Anabel’s take
I’d zoom in to fix a troublesome edge, then zoom out before deciding whether it still needs work. A cutout for a small card needs a clean outline at the size people will see. I’d keep the XCF around for the day that same portrait needs a wider crop.