About the "when" depth limit were issued, I can answer for Italy.
Scuba training here started at the end of the forties (around 1948) thanks to pioneers as Luigi Ferraro and Duilio Marcante.
Scuba Diving Education | Luigi Ferraro
Ferraro was a close friend of Cousteau, and together they had a big influence inside the just-born CMAS, in the fifties.
The didactic standard developed by Ferraro was based on three levels (three "stars" in CMAS).
At first level (novice) there was a depth limit of 15m, buddy was mandatory, and no deco.
At second level (intermediate) the depth limit was 30m, again with buddy and no deco.
At third level (expert) the depth limit was 50m, deco was allowed, but the buddy was still mandatory.
All three levels were fully recreational, "tech" was considered, at the time, only for gas mixtures and depth greater than 50m.
Interesting to be noted that, even at the first level, the certification did also allow for using CC rebreathers in pure oxygen down to 10m. Actually, scuba diving training was mostly done employing these very dangerous CC rebreathers, and only at the end of the course students were allowed to use compressed-air OC scuba systems.This remained unchanged until 1980, so when I was trained (1975-1978) i went through those three degrees., and I was using the CC oxygen rebreather
No one was enforcing the limits, indeed, as scuba diving was a truly DIY experience: there were no "dive shops", no "diving centers", no "professional instructors", as training was entirely done in clubs, by volunteer instructors which were not paid (not they did have any insurance or civil legal liability). Everyone was responsible for himself, both during training and after, and so everyone had to enforce himself his depth limits.
Of course, people were exceeding them systematically.
Hence, already at 1st degree the course was lasting 6 to 9 months, including complete training for deco and repetitive dives the same day, dives in lakes at altitude, etc.
This means that here there was not a time where depth limit started to be employed. They have all been there since the fifties...