The presidential flag actually was changed in 1946 by democratic President Harry S. Truman. He changed the eagle to face toward the olive branch, which, as you know, represents peace. Obviously, this was because we had just finished war with Germany, and then, a few months later, with Japan. As for the other seals, they have pretty much always faced to the left, which is uncommon in seals for birds apparently. The website below reasons that the US did not have many trained heraldic artists. Look for quarters and half dollars from before 1946. Which way is the eagle’s head facing? Also, the Nazi Coat of Arms is inconsistent with direction that the bird faces. Google images of the Coat of Arms. If you think that the Eagle was influenced by this Nazi symbol, you are horribly incorrect.
https://www.americanheraldry.org/heraldry-in-the-usa/official-heraldry-in-the-united-states/the-arms-of-the-united-states-of-america/myths-mistakes-and-misconceptions