Dear
Actually ,when you are a backend designer you must know all this field.But in my company,we divide to many groups,one for PnR,one for STA,DFT.....It means that you have strong knowledge for group which you are belong to.But your work will relate to all others group so you must know everything.To be sure that we can support each others to finish project.
You cannot focus on one of the above and ignore all the rest...
Usually the backend will not do the synthesis... but you should be able to understand it and fix errors if needed.
Usually the back end engineers work begins with a netlist and an SDC file ... which usually has errors... so you should be able to tell them what is wrong
Actually all these processes are interlinked and the final delivery happens after many iterations back and forth, so you need to understand the basics of all these things, so that you would feel comfortable when you actually execute.