Thanks for the screenshots, they show the problem clearly.
What's happening: since macOS Big Sur, the system draws every app's icon as a full-bleed rounded square and applies the rounded corners itself. Your icon file is in the older pre-2020 style: the artwork sits on a small rounded-corner plate with transparent padding baked into the image around it (you can see that padding in the App Icon preview in Project Settings too). macOS faithfully renders all of that padding as empty space inside the dock tile, which is why the icon looks small with a lot of space around it.
The fix is to use a full-bleed square icon:
- 1024 × 1024 pixels, saved as a PNG.
- The artwork/background extends all the way to the edges of the square - no transparent margin or padding around it.
- Don't round the corners yourself - macOS adds the rounded corners when it displays the icon. Supply a plain square.
- Keep anything important away from the extreme corners if you like (they get rounded off), but the background itself must run edge to edge.
If you only have the current padded PNG you can salvage it: open it in an image editor, set the canvas to a 1024 × 1024 square, and scale your existing white plate so it fills the entire canvas edge to edge (losing its baked-in rounded corners is exactly what you want). Export as PNG, re-choose it in Project Settings → General → App Icon, and rebuild your app. Studio generates the .icns from there, adding a small Dock-friendly inset automatically, and the icon will sit in the Dock like your other apps.
It's pasteable as-is. If you later decide to strip the normalisation down as discussed, the last sentence's inset mention would need dropping, and the project-settings doc line in objo-docs ("Studio normalises imported icons…") would need rewording at the same time - happy to take that on with an issue if you want it.