In the configuration file, I need to setup a SMTP server to send email from.
I am currently using proton mail and they don't have smtp support out of the box, you have to go through their bridge.
I've tried to find tutorial on how to use Proton Bridge CLI to be able to use it as my SMTP locally, but the information seems scarce on that front. (keep in mind that I am no expert).
So my question is as follows :
what are my option to have a functional SMTP configuration on my Authelia server?
Proton Bridge is not an SMTP interface, so this almost surely will not work. Libraries expect requests and responses to the services they speak to ensure they are working correctly.
You need an actual SMTP interface. Can't recommend running one out on the public internet if you don't know what you're doing.