Only four rooms of the town museum are devoted to Bach's time, and much of the display is concerned with Prince Leopold rather than with Bach. But without Leopold's interest in music – and his desire to be seen to have the best of everything – Bach wouldn't have had a job, so the information is very relevant. Someone came and opened up the museum for me, and provided a very interesting audio guide in English which talked mainly about Bach in the context of Leopold's reign, as I padded around the paintings and furniture wearing huge felt slippers over my shoes to protect the floors.
There were clearly very good players in Prince Leopold's orchestra, and as a competent viola da gamba player he would have wanted to join in from time to time. Brandenburg Concerto no. 6 includes two gamba parts, one of which is relatively easy compared to the virtuosity required for the other instruments (and the gambas take a break in the second movement) and it may well have been intended for Leopold.
Prince Leopold rather lost interest later in life, being distracted by increasing delusions of grandeur in ruling a principality of just 10,000 people (Anhalt-Köthen) in the style of the leader of a large country. There's a painting of him, for example, with the then 'exotic' black servant, aping the paintings of the more important leaders of the time.
1721 is the year that Bach's music changed from orchestral pieces to solo works, such as the cello suites, probably reflecting Leopold's change of priorities. The cello was a new instrument at the time. Leopold would have been keen to show that he was up to date, buying an early 18th century instrument by Stradivari, and Bach writing the perfect music for it.