A popular standalone printf-family library in the embedded world is, well, printf :

https://github.com/eyalroz/printf

which is independent of a C standard library (it doesn't actually do any I/O itself). Originally by Marco Paland, now maintained, or 'curated' by myself (so, this is a bit of a self-plug, even though I can barely claim authorship). It offers this generalization :

  int fctprintf(void (*out)(char c, void* extra_arg), void* extra_arg, const char* format, ...);
  int vfctprintf(void (*out)(char c, void* extra_arg), void* extra_arg, const char* format, va_list arg);

  typedef struct {
    void (*function)(char c, void* extra_arg);
    void* extra_function_arg;
    char* buffer;
    printf_size_t pos;
    printf_size_t max_chars;
  } output_gadget_t;