The $TD(0)$ algorithm learns from incomplete episodes, but in the earlier algorithm we can see that the loop repeats until $s$ is terminal which mean completion of episode.
In the pseudocode, you have two loops: one for each episode and one (nested) for each step of the episode. The until $S$ is terminal means that you perform the updates until you end the episode (that is, you end up in a terminal state, e.g. checkmate in the game of chess). For each step of the episode, you perform the TD(0) update.
Apparently, you're confusing two things: the fact that each episode ends in a terminal state and the fact that TD learns from incomplete information. Each episode ends in a terminal state (otherwise it would not be called an episode), but this does not mean that it collects a full rollout before updating $V$. In fact, at each step of the episode, it updates $V$.
The information in the David Slider's slide is consistent with the pseudocode. TD learns from experience because it uses the given policy $\pi$ to behave.
learning from incomplete episodes, mean learning of $V(s)$ even when the episode is not completed
Yes, essentially you're updating the value function during each step of each episode.