A trivia question for you:
Who wrote Bach's Toccata and Fugue in D Minor?
If that sounds silly, you may not have encountered the earnest discussion about this piece, which has been taking place since the 1960s. The current Wikipedia article points out that this piece of music was not published until 1833, during the revival of interest in Bach's music, fostered by Felix Mendelssohn and others.
Bach wrote over 2000 pieces of music, of which we have about 1080. Probably many of the ones that are lost are recyclings of existing works. Bach recycled his music like I recycle jokes! A true Eighteenth Century greenie!
But only twelve of his works were published in his lifetime, and he had to pay for half of those to be engraved!
Many scholars think that this piece of music is not in the style of the great master's other organ works and sounds like it was created later than Bach's lifetime by an anonymous composer. Others say it is a transcription, maybe by Bach, of a lost solo violin piece.
But distinguished Bach scholar Christoph Wolff is happy to ascribe it to Bach, but in his early days.
It would be disappointing if one of the few universally known pieces by Bach was in fact written by someone else!