Apologies, I forget not everyone has beaten their heads on authentication before. Oops.

I have no idea what cURL is or any of that, unfortunately. I couldn't tell you what's going on under the hood. However, the troubleshooting you've done leads me to believe it's the job causing the issue, not the code itself. The most likely problem when you can manually run something, but a job can't, is one of a few issues.

First, a job runs under the authentication of the SQL Agent. That Agent has a login defined in the services on the box it's installed on. You need to find out that user, and confirm that they have equivalent access that you do to be able to run all the necessary pieces. It may not have access to one or more files/directories.

If that's all well and good, then you need to determine if you're dealing with a Kerberos double-hop issue. Google that and you'll find reams of information on the problem, but the root cause is this: If your network isn't setup the way you need, authentication only can visit one server out. Otherwise it needs the equivalent of a repeater to send that security token to the next place. So, if your .bat is then calling for something on another machine, it may (note, may. Talk to your sysadmins) not be able to pass it along to the next one. Usually my office uses wireshark to determine when there's a problem of this nature.

From there, keep examining security possibilities. That is the 99% cause (in some form) when SQL Agent won't work, but you can manually run things.