Bohr does not think that quantum mechanics shows that there are gaps in the causal nexus that give room for freedom of the will. He does believe that humans have genuine agency, but he doesn’t think that’s something that was only substantiated by physics in the 20th century.
Bohr thinks that the very idea of an experiment presupposes that the experimenter has free will.
Bohr thinks, in particular, that the experimenter is free to choose the settings of his experiment — which, in formal terms, corresponds to the basis relative to which the situation should be described.
Bohr shows some sympathy for the idea of psycho-physical parallelism.
Bohr thinks that the concepts of free choice and causal determination are mutually exclusive. Nonetheless, he thinks that both concepts are indispensable for a full understanding of human psychology.
“In particular, the place left for the feeling of volition is afforded by the very circumstance that situations where we experience freedom of will are incompatible with psychological situations where causal analysis is reasonably attempted. In other words, when we use the phrase ‘I will’ we renounce explanatory argumentation.” (Bohr 1948 p 318)
“Just as the freedom of the will is an experiential category of our psychic life, causality may be considered as a mode of perception by which we reduce our sense impressions to order. At the same time, however, we are concerned in both cases with idealizations whose natural limitations are open to investigation and which depend upon one another in the sense that the feeling of volition and the demand for causality are equally indispensable elements in the relation between subject and object which forms the core of the problem of knowledge.” (Bohr 1934 p 116-117)