Emphasis depends on what else is on the screen.
The common read: If a reviewer can see the difference between two colours, users will spot the one that matters in a full screen.
Whether a target pops out depends on the target and on the display around it, and a design review that compares two swatches never looks at the display. Search efficiency rises with the difference between the target and the distractors and falls with the difference among the distractors themselves, which means the same accent colour can be found instantly on one screen and be invisible on the next.
A second condition has more direct design consequences. When the difference between the target and the distractors is large enough, search is efficient if the target is linearly separable from the distractors in the feature space: a line can be drawn with the target on one side and every distractor on the other. Separability does not make up for a difference that is too small. The overdue red in the first question is separable from the ordinary red, and operators still miss it.
When the distractors flank the target, search becomes inefficient. An accent whose colour lies on the straight line between two accents you already ship, in a two-dimensional colour space, is the flanked case. Saturation is one of the two axes of that space, so making the accent clearly more saturated than both can move it off the line and make it separable again. This works only if the difference is also large.
The thresholds are also much larger than most people expect. For orientation, the reported critical difference for efficient search is around fifteen degrees, far larger than the smallest tilt a person can detect, and guidance is categorical rather than metric: search is more efficient when the target is uniquely steep or shallow. Colour behaves the same way, and the researchers say so directly: the metrics of colour difference for foveal discrimination are quite unlike those that govern the deployment of attention.
A common failure: a ticket titled "make the overdue state more obvious" is assigned to whoever owns the palette, closed by a hex change, and reopened next quarter with the word "still". Before you add an accent, count the accents already on the screen, and check that the new colour differs enough from every other element competing for attention, not only from the background.

