Context in Module B is relevant only if it contributes to your own critical reading of the play. For example, if you were to read Othello as a play about racial prejudice, you would spend a paragraph or less discussing the status of North Africans in Venice during the 16th century, and how the character Othello highlights their exclusion from Venetian society. Contextual discussion for Module B is incidental - that is, it is inevitable that you touch on it as you elaborate on your critical reading, but it is not something you deliberately focus on as it is with Module A.
In this band 6 essay introduction on the 2014 Module B question on Hamlet, you can see that the thesis is based on how the characters demonstrate values of nobility and glory
dominant in the 16th century. In the essay body however, you are not going to be discussing those values at length (such as tying them to specific events or movements), and how the composers challenge those values as you would for Module A. It's enough to just emphasise that
what those values are, then move on to how techniques and language features are used to represent conformism to those values (Fortinbras and Laertes) and subversion of them (Hamlet).
As for Shakespeare's sources, they are important when considering his context only if they relate to wider contextual issues/events - e.g. for Julius Caesar, the fact that Shakespeare's primary historical source Plutarch is worth analysing briefly because of
the wider contextual event of a revival of interest in ancient Greek and Roman thinkers during the Renaissance.
For Romeo and Juliet, the fact that Shakespeare borrowed the plot of the play from Masuccio Salernitano is relevant only if you are going to discuss it
in terms of what Shakespeare changed about the original Italian plot to make it more appealing to his English audience - that is, what issues/preoccupations did he put into his version of the Italian story so that it reflected the values/interests of his English audience?