I participated in Google Summer of Code and received a stipend from Google. I worked with volunteer mentors associated with free/open source projects not associated with Google in any direct way.
Is GSoC considered an internship, a job, or any form of employment?
No. GSoC is an activity that the student performs as an independent developer for which they are paid a stipend.
As far as I could determine, the form of self-employee closest to describing a GSoC student is "independent contractor". However, I am uncertain that it fits completely. The definition I found says:
The general rule is that an individual is an independent contractor if the payer has the right to control or direct only the result of the work and not what will be done and how it will be done.
Google did not really control or direct the results or anything about the work.
Is participating Google Summer of Code considered "self-employment" under US tax law?