Thanks for your input, you pointed the right direction ! After some more reading, this is what I found.
Adding the following line in sudoers file after @includedir /etc/sudoers.d:
server ALL = NOPASSWD: /usr/lib/openssh/sftp-server
Works without the need of a sudo session for the sftp-server. I have no idea if this is good security practice but If i had to guess I would say no. Having the NOPASSWD argument for something critical as an ftp server seems… Not a good idea ! But I’m not an expert, so I’m just guessing :/.
If I may, how would you tackle such an use case ? My first solution seems way more secure with the right permissions on the bind mount, what do you think ?