Take anything I say as coming from someone learning all this too and trying to synthesize it, happy to be corrected.
Re-reading the general and max strength on page 266 I am seeing this referring to the gym based workouts. As I noted above the stage 3 appears to be the max strength component, but that is a touch confusing as page 266 seems to be the only place max strength is mentioned, though emphasized as distinct in TFTNA. In TFTNA both gym based and the sport specific 10 sec hill sprint progressions (reps/sets, not time) are categorized as max strength.
On pg 266 Z4 and Z5 are listed separately. Z5 mentions hill sprints as sport specific strength at 10-30 sec. However, page 183 discusses Anaerobic Endurance as to two general classes of interval training, one based on 2 min intervals and one based on 20-30 sec intervals, which include both the Z4 and Z5 listed on page 266. 10 sec hill sprints/bounding is also found under anaerobic intervals starting and on page 180 the first paragraph clearly describes the training effect in early intervals as neurological recruiting more fast twitch motor units.
Obviously all these are on a continuum of stimulus with some overlap of training effect. My takeaway is:
-hill sprints/bounding is a form of sport specific max strength and anaerobic interval
-the farther you move past 10 sec the more of an anaerobic endurance/metabolic stimulus is created
-max strength is emphasized in base and intensity phases, moving from gym based towards sport specific methods. If using hill sprints for this effect keep them to 10 sec and increase the number of reps/sets as outline on page 182.
-past 10 sec the anaerobic stimulus overtakes the neurological/max strength stimulus and should be reserved only for specificity phases of training, and even then in better trained athletes with more base or multiple yearly cycles under their belt. The mike foote plan progression increases # reps and time from 15 sec in increments up to 2 min.
As an aside, I consider my self transitioning from beginner to intermediate, and did only a portion of the progressions in the Mike Foote plan this year — namely no longer anaerobic intervals. I did however carry the 10 sec hill sprints and bounding through later phases of training where more advanced athletes might switch to longer intervals. I found these workouts really fun and energizing.
Regarding your last question, the phrasing of the Strength entry in the Intensity week on page 295 suggests runners can do either hill sprints or bounding, but that ski mountaineers would benefit more from hill bounding.
I found this podcast to be very helpful and entirely consistent with UA advice.
https://www.scienceofultra.com/podcasts/95