For a small camera, normal running vibration is unlikely to cause damage if it’s packed properly. The bigger issue is usually poor packing: if the camera is bouncing around, the bag or load setup isn’t secure enough.

Use a backpack that fits snugly, keep the load stable, and avoid empty space that lets the camera move. Putting the camera in a padded pouch, or wrapping it in a sweatshirt/jacket inside the bag, will reduce jostling and impact. Also keep other hard objects away from it.

In general, compact and small interchangeable-lens cameras should tolerate this kind of movement reasonably well. A camera loosely knocking against your back every step is more likely to be uncomfortable for you than harmful to the camera.

So yes—bringing a small camera on a run is usually fine, as long as it’s immobilized and cushioned rather than allowed to bounce inside the pack.