The opening fanfare is Abblasen by Gottfried Reiche. Reiche was Bach’s trumpet player at Leipzig. Trumpet players were highly paid, and had their own guild, as the instrument was/is so difficult.
Sunday morning used an authentic version played by Don Smithers on a natural trumpet as used in Bach’s time (no valves). I miss it.
They switched to a decidedly unauthentic version played by Doc Severinsen on a piccolo trumpet and now use a recording of Wynton Marsalis on piccolo.
The piece is not all that hard, but keeping everything in tune is difficult.
Neat trivia, the piece is from a painting of Reiche in which he holds a bit of music, similar to the painting of Bach holding a sheet of manuscript.
Probably more than you wanted to know from a trumpet nerd.