TAINT_WARN is explained in kernel/panic.c as ‘Taint on warning’.

static const struct tnt tnts[] = {
...
  { TAINT_WARN,     'W', ' ' },
}
  
/** 
 ...
 *  'W' - Taint on warning.
 ...
 */

This flag is turned on from “__WARN()” to confirm that the system had ‘WARNING’ messages once or more time.

#define __WARN()    __WARN_TAINT(TAINT_WARN)

#ifndef WARN_ON
#define WARN_ON(condition) ({           
  int __ret_warn_on = !!(condition);        
  if (unlikely(__ret_warn_on))          
    __WARN();           
  unlikely(__ret_warn_on);          
})
#endif

#define WARN_TAINT(condition, taint, format...) ({         
    int __ret_warn_on = !!(condition);              
    if (unlikely(__ret_warn_on))                    
        __WARN_printf_taint(taint, format);         
    unlikely(__ret_warn_on);                    
})


#define __WARN_printf_taint(taint, arg...)        
  warn_slowpath_fmt_taint(__FILE__, __LINE__, taint, arg)
  

void warn_slowpath_fmt_taint(const char *file, int line,
           unsigned taint, const char *fmt, ...)
{
  struct slowpath_args args;

  args.fmt = fmt;
  va_start(args.args, fmt);
  warn_slowpath_common(file, line, __builtin_return_address(0),
           taint, &args);
  va_end(args.args);
}

static void warn_slowpath_common(const char *file, int line, void *caller,
         unsigned taint, struct slowpath_args *args)
{
  const char *board;

  printk(KERN_WARNING "------------[ cut here ]------------n");
  printk(KERN_WARNING "WARNING: at %s:%d %pS() (%s)n",
    file, line, caller, print_tainted());
  board = dmi_get_system_info(DMI_PRODUCT_NAME);
  if (board)
    printk(KERN_WARNING "Hardware name: %sn", board);

  if (args)
    vprintk(args->fmt, args->args);

  if (panic_on_warn) {
    /*
     * This thread may hit another WARN() in the panic path.
     * Resetting this prevents additional WARN() from panicking the
     * system on this thread.  Other threads are blocked by the
     * panic_mutex in panic().
     */
    panic_on_warn = 0;
    panic("panic_on_warn set ...n");
  }

  print_modules();
  dump_stack();
  print_oops_end_marker();
  add_taint(taint);
}

void add_taint(unsigned flag)
{
  /*
   * Can't trust the integrity of the kernel anymore.
   * We don't call directly debug_locks_off() because the issue
   * is not necessarily serious enough to set oops_in_progress to 1
   * Also we want to keep up lockdep for staging development and
   * post-warning case.
   */
  if (flag != TAINT_CRAP &&
      flag != TAINT_WARN &&
      flag != TAINT_TECH_PREVIEW &&
      flag != TAINT_HARDWARE_UNSUPPORTED &&
      flag != TAINT_TECH_PREVIEW &&
      __debug_locks_off())
    printk(KERN_WARNING "Disabling lock debugging due to kernel taintn");

  set_bit(flag, &tainted_mask);
}