Does burst mode reduce image quality on later shots of a still scene?

This depends on the specific camera model. Different cameras have burst modes that work in different ways, which may affect the image quality.

Many cameras have options for the burst rate, ie high, medium, low. Typically the lower speed is just the same as taking standard photos in series. So the quality is just the same as a single photo.

But the faster burst rates may have limitations. For many cameras, the fastest burst rate is at a lower resolution, and often more compressed, so a clearly a lower quality image. Also it probably won't allow shooting in RAW format, only JPEG.

Often the focus will be fixed at the start of the burst, it won't change in following shots. This would be fine if the camera and subject are stationary, but if not, they could move out of focus.

Some mirrorless cameras will use an electronic shutter for faster bursts. This can cause strange effects for moving subjects, or under fluorescent lighting.

To find out how your camera works for burst mode, you can read the manual, or just try taking some test shots at different speeds.