Your M&P is definitely from late in the production run. S&W stopped manufacturing .32-20s in the 1929-30 period, but they sold out of remaining inventory stock until WWII, so yours may well have shipped from the factory sometime in the 1930s. There is one known case of a .32-20 M&P shipping from the factory in 1965. The closest .32-20 M&P SN on my list to yours is 1413xx which shipped in 6/1929, so yours would have been made prior to that.
S&W M&Ps in .38 Special outsold those in .32-20 by a factor of about 4:1 during the period of .32-20 M&P manufacture, so they were not too popular with the public and were slow movers. While M&Ps in both calibers were essentially identical except for chambering, they were separately serial numbered. Colt's made several models of their revolvers chambered for the .32-20, but they also ceased production due to lack of demand by sometime in the mid-1930s.
As you may have discovered, .32-20 ammunition is somewhat expensive and difficult to find today, even though it is still loaded.