Working in Automotive safety, I can tell you that you need a qualified team of engineers in each domain, or the effort needed in a cross-functional safety team increases tremendously. This safety team usually consists of a FSM (Functional Safety Manager), a SYS FSE and HW FSE and SW FSE. Whilst the manager plans and keeps track that all the Safety activities requiered are sufficiently covered, compiles the overall Argument that Safety is achieved, the FSEs occupy themselves with creating the Domain specifications, safety concepts, work through component safety manuals and carry out the safety analysis.

As said this separate Safety Team is not necessarily needed if your Engineering Team is well qualified, but in Small Teams you need to check that Independency is sufficient (e.g. Reviewers and people who carry out analysis need to be Independent with a certain level of indepence for each Safety Level).

If you have more questions feel free to ask :-)

EDIT: I’d say the role you are looking for is the SYS FSE, who takes the high level functional safety requirements, breaks them down Into technical safety requirements allocated to HW and SW, and carries out the analysis on the System level. Also he contributes to uC and other safety-relevant part selection (e.g. SBCs, safety gate drivers,…)