At What Speed Does The Milky Way Move Through Space?

If the milky way is moving through space, are all other galaxies surrounding the milky way moving at exactly the same rate? It seems that if the milky way is moving through space, the environment outside the milky way would change as it moves through different areas of space. Does this happen?

Astronomers think the Milky Way is traveling at around 600 km per
second (which is 1,342,161 miles per hour) relative to the locations of other galaxies.

Recent estimates range from 130 km a second to 1,000 km a second.

If the Galaxy is moving at 600 km/s, Earth travels 51.84 million km per
day (32,211,882 miles, or more than 18.9 billion km per year (1.17439155 × 10¹⁰ miles).

Sources: Wikipedia -  Milky Way,  public.iastate.edu