In the first movement of his Trumpet Concerto -  what did Haydn mean by the intro  (bar 8 + bar 13 - 16 - see above)?

Was it maybe a "Haydn joke"?

Did he mean to say "Good bye!" to the old trumpet with its broken triads and fanfares?
Or was it to make the listener believe that this was another typical concerto for an instrument only capable of some few natural harmonics? Then when the solo starts: SUPRISE! -  this is a new instrument capable of playing all the notes, even chromatic.

No one knows - but it is a strange part of the concerto. In modern performances these notes are often left out by the soloist. In some editon it is also left out of the solopart.

William T. Greene has another explanation ("The Haydn Concerto in Performance" page 52 - 53):

"The opening of movement one from measure 8-16 contained notes available to the natural trumpet."

"At measures 37-40, the solo exposition began with notes in a ditonic arrangement"

"Then at bar 47, the cromatic descent by half steps completed that demonstration. "

"Haydn had carefully introduced the keyed trumpet: first with natural figures, next with diatonic notes, and then with a cromatic passage"