Disclaimer
Dear commenters, I have done very little research on this topic, and I am not a computer scientist. Just an average programmer who has written at most a few hundred lines of C. Feel free to (politely) tell me all the ways I am wrong.
As long as you're turing complete
I think you can stop there. Any computable function can be run on any Turing complete machine. You just need the right machine code. So you don't really need to add further qualifications.
However, if you do... If you say C needs to be able to read input, write to files and devices, allocate and randomly access memory, or talk to an operating system in any way, then you've tied it to a particular (abstract) architecture. So, I'd say that's a pretty low level language on the abstraction spectrum. Most other languages are higher than it. If you were to rate programming languages from 0 to 10, C would be about a 3. Maybe even 2 for kernel code. Python would be like a 7, and SQL would be like an 8.
Anyone saying a language is strictly either "high" or "low" is missing a lot of nuance, and C is definitely on the low end.