I just put in your query (i.e. "Bourbaki was founded ..., young university instructors were forced to use dated texts") into Google AI Mode to explain with references/links/citations which it did reasonably well. The main points are;

1) It was in late 19th century/early 20th century that the german (and other european) mathematicians (Hilbert et al.) revolutionized rigour in the teaching of mathematics with the establishment of definition/theorem/proof (DTP) "new math" style which we understand today as the norm.

2) WWI (1914-1918) wiped out over half the french mathematicians from the various top french mathematical training academies. This was the "lost generation" creating a demographic gap of mathematicians who were trained in the new style above.

3) Thus in mid-1930s you had only a small group of young french mathematicians (Cartan, Weil etc.) who were exposed to the rigorous style now pushed into professorship positions. However their previous generation being lost in the war meant most books were from 19th century written using the "old style math" (i.e. less rigorous). Eg. Standard french university textbooks on Calculus/Analysis were by Edouard Goursat rooted in old 19th century concepts. Hence they are frustrated and start writing books under the Bourbaki name to reestablish french mathematics rigorously.

So a generational crisis (i.e. loss in war) happens when mathematics undergoes a fundamental shift. This leads to books becoming outdated. Young french mathematicians inspired by german abstract school set about unifying all of mathematics using the new rigorous style in terms of various abstract mathematical structures.