> system call, the context switches

No, there is no separate kernel "executing". When you do a syscall, your thread becomes kernel mode and it executes the function behind the syscall, then when it's done, your thread reverts to user mode.

A context switch is when one thread is being swapped out for another. Now the syscall could internally spawn a thread and context switch to that, but I'm not sure if this happens in read() or any syscall for that matter.