Derailleurs were not allowed in the Tour de France until 1937, and so were not really part of the mainstream racing scene until that date.
At the same time derailleurs were not viewed as being appropriate for everyday bikes - the exposed chain required too frequent oiling, picked up grit and wore out too fast and dirtied your clothes - much better to have a fully enclosed chain case and a three speed hub gear.
So the development of derailleurs during the 1930s was left to the (much loved) lunatic fringes of cycling, the cycle tourists, the tandem riders, the plain mad inventors and those racers who just could not resist stretching the rules (modern patron saint - Graeme Obree). For this reason the 1930s is viewed by many as a golden age of innovation and development.
Certainly many of the companies that dominated the next few decades established themselves in the 1930s, moving from the garden shed to the small factory.
In terms of technology, the braze-on fitting under the chainstay became a touring/tandem standard, and the, hub-axle-fitting, pull-chain derailleur became a recognised form for lightweight bikes.
When derailleurs were, finally, allowed in the Tour de France they proved to be essential to any chance of winning, and overnight became an accepted part of a racing bike.
Browse the derailleurs from the 1930s...
Where you see a red link, this is for a derailleur model which I do not (yet?) have in my collection - but for which I do have some kind of real and relevant documentation.