More of a suggestion than a clear critique:
ShellCheck (https://github.com/koalaman/shellcheck) is super helpful to catch small errors in bash code, as I mentioned via slack, I highly recommend running it over the project.
It integrates with most editors if you're interested in that.
It mostly helped me find some issues in your code where you should be encapsulating variables with " quotes, and that there are a few unused variables.
For example, the following I believe should be encapsulated with quotes around variables:
https://github.com/4rnaudB/spinalcord-signal-recovery/blob/2a63e5a8fa01b0062fb0e6f176706bc49ea7a754/scripts/experiment_script/run_experiment.sh#L77C1-L77C73