The stock pays a 6% dividend per year by law.
... and the fact that Congress even retains control of management. The only reason banks buy shares is so they can "avail themselves of the advantages of this Act."
Each of the 12 regional bank districts is operated by a 9 member board of directors. 3 of the members are appointed by the board of governors of the FRB and 6 are elected by the member bank that own stock in the regional bank. Each District has at least one branch (most have multiple). Each branch also has a board of directors. The branch board of directors are appointed by both the FRB district bank (they appoint the majority) and the FRB board of governors (they appoint the remainder). These directors are involved in formulating monetary policy. While true that congress could over-rule anything the FED decides to do, it generally doesn't.
If you've got a link to that law please share, though what we're talking about is ownership that provides control. Dividends don't constitute ownership and control; think-- savings bonds.
directors are involved in formulating monetary policy
Sort of. What they do is participate in the activity of the setting of monetary policy (from here). The FOMC makes policy. If Congress doesn't like the FOMC's policy then they can abolish the Fed. The stockholders have about as much control as someone who writes a crank email the the Fed -- which is yet another form of participation in the activity of the setting of monetary policy.