Hello,
Draw() will repeat 60 fps (frames per sec) unless something is blocking it or slowing it down.
In your code, the while() must complete before it exits and continues to the code in draw().
This may be why you have to wait; this is blocking code while serial data is being received.
Here is an example:
Arduino Code
int count;
void setup() 
  {
Serial.begin(115200);
  delay(1000);
  Serial.print('\n'); //same as Serial.println()
  Serial.print("incoming");
  Serial.print('\n'); //same as Serial.println()
  }
  
void loop() 
  {         
  Serial.print(count++); 
  Serial.print(',');
  for (int i = 0; i<1000; i++)
    {
    Serial.print(i);    //same as Serial.println()    
    Serial.print(',');
    delay(10);       
    }
  Serial.print('\n');   //same as Serial.println()
  delay(10);
  }
Arduino sends 1000 strings (from 0 to 1000) with a 10 ms pause between strings so this will take around 10+ sec to send.
Processing Code
import processing.serial.*;  
Serial myPort;
String val;
void setup()
  {
  size(700, 700);
  background (0);
  
  colorMode(HSB, 360);
  
  // List all the available serial ports
  printArray(Serial.list());
  
  String portName = Serial.list()[4];
  myPort = new Serial(this, portName, 115200);
  }
void draw()
  {
  //if (myPort.available() > 0)      //not blocking
  while (myPort.available() > 0)   //blocking
    {
    val = myPort.readStringUntil('\n');
    if (val != null)
      {
      println(val);
      }
    }
  plotting();
  }
void plotting()
  {
  background(random(360), 360, 360);
  //println("Plotting");
  }
Processing receives the data.
A while() loop (blocking) waits until all the data is received and then continues to plotting() which changes background every 10 sec.
An if() loop (not blocking) allows plotting() to execute and the background to be changed with each draw() cycle (60 fps).
You will have to wait until the first string is received in my example to see the blocking vs not blocking effect.
My preference is to use:
https://processing.org/reference/libraries/serial/serialEvent_.html
:)