Whether or not "using an API" requires your software to be GPL depends on how it's implemented.
Going by GNU's description of what does and does not extend the GPL requirement[1] and how Blender plugins works, to me at least it seems they very clearly have to be GPL. Unless someone took the route that is common in closed source Linux drivers of having a small open source module that communicates with a binary blob where the majority of the actual interesting code is, but I have not seen any Blender plugins like that.
The Linux kernel actually provides a specific license exemption[2] for the headers that makes software using syscalls not bound by the GPL.
Actually this is exactly what we did with the renderman addon for Blender. And AFAIK how other renderer addons work.
Frankly if you want to be doing any meaningful computation in your addon it probably makes sense to go this route and have the closed source part in C while the addon "bridge" is python.
Going by GNU's description of what does and does not extend the GPL requirement[1] and how Blender plugins works, to me at least it seems they very clearly have to be GPL. Unless someone took the route that is common in closed source Linux drivers of having a small open source module that communicates with a binary blob where the majority of the actual interesting code is, but I have not seen any Blender plugins like that.
The Linux kernel actually provides a specific license exemption[2] for the headers that makes software using syscalls not bound by the GPL.
[1] https://www.gnu.org/licenses/gpl-faq.en.html#GPLAndPlugins
[2] https://www.kernel.org/doc/html/v4.18/process/license-rules....