Depends on the distance. But here is the just of it for me:
The warm-ups are key for anything faster than "long run" pace which includes HM Tempo, Daniels T, and Tempo. Essentially, there are two main pathways for the body to use oxygen to produce energy. The aerobic pathway is mostly used in slower running. The closer you get to the point where it becomes harder to breathe (Ventilatory Threshold) the more you use the anaerobic pathway. The aerobic pathway is more efficient and faster at creating energy, whereas the body uses anaerobic when the aerobic can't keep up (because you're going too fast).
The most interesting part between the aerobic and anaerobic pathway is that even though the aerobic is used mostly during slow running it takes about 6 minutes of running before it can be used. This means for the first 6 minutes we're stuck with the slow, inefficient anaerobic pathway. So if you don't do a warm-up, and you're running faster than "long run" pace (about MP + 9%) you push the anaerobic pathway too hard. This creates a deficit in energy within the first 6 minutes that becomes harder to overcome. As this deficit starts to catch up with you in later miles, it causes our running form to suffer.
I do dynamic stretching before all of my races. I suggest my runners do whatever pre-training run stretching routine prior to the race as well. So some stretch. Some don't stretch. Good research to show that changing the routine is more likely to lead to injury than either to stretch or not stretch.
After the dynamic stretching comes the race day WU. If the distance is a 5k, I'll probably do 30-40 min of running at a very easy pace (like 20% slower than marathon pace). For 10k, maybe 20-30 min. For HM, maybe 10-20 min. For M, I usually only do about 6-10 min. The pace isn't super important as long as it isn't faster than MP + 20%. If my body thinks easy is MP + 30%, then I go with that. Towards the end of the WU is when I'll add some strides in. Strides are short bursts of speed lasting in total duration of no more than 10 seconds. Three seconds building pace, three seconds holding pace, and three seconds of gradually slowing down. These are a neuromuscular stimulus. You've likely tapered leading into race day. Which means you were likely doing a lot of easy running the last few days/weeks. These strides reawaken the muscles to say, hey guys it's race day. I do maybe 4-5 strides in total with at least 45-60 seconds between them. The goal is not to be super fast and burn up energy. It's meant to be short and sweet. I start this entire running WU no sooner than 60 min to race start. I finish the WU no closer than 15 min to race start. Earlier than 60 min and the WU loses its effectiveness. Closer than 15 min and you start to infringe on your racing ability.