Finding the right bottom bracket crankset combo
Your bottom bracket is screwed into the eccentric. You'll be replacing the bottom bracket. The fact that it's in an eccentric doesn't affect the part choice. The eccentric is more like part of the frame.
To install FC-S501 you need any Shimano road Hollowtech 2 BB, as indicated by BB-SM4600 being the model called out in the Shimano exploded view diagram for it.