Shutter speed can affect sharpness in a few ways:

Camera movement - intentional or not. People aren't 100% steady, that's unintentional movement. Some tripods aren't very steady either. On the other hand you might be tracking a moving subject. That's intentional, and you're expecting the background to be blurred, but if your tracking isn't absolutely perfect, you may see softness in the subject with lower shutter speeds.

Subject movement - I need to use 1/2000s or so to ensure I get sharp pictures of my dogs. They're pretty fast. That's probably a mix of panning, and subject movement.

Mirror bounce - When the mirror in your camera moves up to take the picture, it introduces a small shake that can affect sharpness with lower shutter speeds.

At higher ISO there will be more noise, and the noise reduction will soften the image. Since more reduction occurs at higher ISOs, there is more softness. The slight softness you see from high ISO is preferable to the ruined shot from too low a shutter speed, or too short an exposure and attempting to brighten in post.