I don't know SE but is it not in general tipped towards 'conditioning' rather than pure strength?
It's pretty easy to thrash yourself to bits with cardio output affecting form. And here, various SF under the umbrella of SE templates are appropriate. But pull ups? Gtg, 5x5, ladders, fighter would apply, no? Whatever is the best fit at a given time.
How would a SE template for pull ups differ?
Pavel specifically designed templates to enhance strength endurance required to hit "high" pullup numbers. The thinking is that there is a limit to the number of reps you can hit training what you are referring to as "pure strength" >25 reps I believe is the rule of thumb. Beyond that you shift your adaptation targets (IIA and IIX MT respiration in strength exercises, myoglobin, strength endurance, synaptic facilitation, myelination, IIA hypertrophy).
The template I'm referring to (#7) is a series-based. The number of reps per set, sets within a series, and total number series are calculated from your RM. The template also prescribes rest between sets and rest between series along with; tempo, speed, intensity, metabolic intensity, the appropriate associated muscle fatigue, breathing rate and training frequency.
You'd need to be proficient then doing explosive pull ups then, presumably.
Multiple times. Big ask for most I'd think.
To answer the specific question regarding required speed of the movement; yes the pull-ups need to be executed in the "moderate to explosive" range. This is not a big ask for folks who are looking to use this plan i.e. >25 reps.
It's pretty easy to thrash yourself to bits with cardio output affecting form.
To address the concern about form breakdown; there are specific "stop signs" for strength endurance exercises' sets and series. If you meet any of the 5 conditions the set / series is terminated.
Hope this answers the questions. I'm more than happy to answer follow-ups or continue this conversation by PM or email exchange.
This is just a drop in the ocean of SE knowledge...