Two floating point values do not get added and printed on ESP-WROOM-32
Try doubles instead of floats. 

Your initial value, 34567891.234 needs 35 bits of precision to keep track of the decimals, but floats only have 24 bits pf precision. So to have enough precision to keep track of the difference between 34567891.234 and 34567891.234+1, you need higher precision storage.

void setup() {
  // put your setup code here, to run once:
  Serial.begin(9600);
}

void loop() {
  // put your main code here, to run repeatedly:
  double a=34567891.234;
  double b=2.3456;
  a++;
  Serial.print(a+b, 4);
  Serial.println("");
  delay(1000);
}