Hello @LouisLoode 
Yes indeed, curl requests should be working !
The issue you are facing here is that brave prevents you from executing requests to a non https url (for security measure).
I don’t know how to configure brave to be honest, however, I’m pretty sure you can work with some config to let this use case work on at least app.forestadmin.com.
An other solution would be to have kind of reverse proxy, meaning that on your local machine you would have a url over https, that would redirect to your local server (by using nginx for instance, or ngrock).
If you find any configuration on brave that works for you, please don’t hesitate to post the solution here, other people could be interested.
Thanks !
Steve.
P.S. I have found some resources that could raise your interest Permissioning access to localhost connections · Issue #27346 · brave/brave-browser · GitHub