The EAD is unrestricted. However, Amazon and other big companies must make sure to comply with export license regulations if they decide to hire a person who is not citizen or permanent resident.
In the job applications, mention that you do not require sponsorship and that's enough to say. There are some jobs, especially in places that are affiliated with the government, that only hire citizens.
bear in mind that some recruiters are very ignorant about immigration stuff all they know is that GC=stay forever. I'd say if you applied to a small company in a rural place just tell the hiring manager that I have a GC on the way and I have work authorization in the meanwhile and explain that it's renewable every 2 years. Later when you fill I-9 form on your first day, give them the EAD.