I am trying to understand the algorithm for n-step SARSA from Sutton and Barto (2nd Edition). As I understand it, this algorithm should update n state-action values, but I cannot see where it is propagated backward. Can someone explain to me how that works?
The important part, where you can see a single reward value is used for $n$ different updates, is the part where a sum of $R_i$ values with $i$ ranging from $\tau + 1$ to $\tau + n$ is assigned to $G$.
So yes, the outer loop of the algorithm always does at most one update per iteration, but for that update it uses multiple previously observed $R_i$ values. Each of those $R_i$ values is used for multiple updates (not multiple updates at the same time, but multiple updates spread out over different iterations).