Try this code and let me know if it works:

#include "SevSeg.h"

SevSeg sevseg1; //Instantiate a seven segment controller object
SevSeg sevseg2;

void setup() {
  byte numDigits = 4;
  byte digitPins1[] = {2, 3, 4, 5};
  byte segmentPins1[] = {6, 7, 8, 9, 10, 11, 12, 13};
  byte digitPins2[] = {14, 15, 16};
  byte segmentPins2[] = {17, 18, 19, 20, 21, 22, 23, 24};

  sevseg1.begin(COMMON_ANODE, numDigits, digitPins1, segmentPins1);
  sevseg1.setBrightness(90);

  sevseg2.begin(COMMON_ANODE, numDigits, digitPins2, segmentPins2);
  sevseg2.setBrightness(90);
}

void loop() {
  static unsigned long timer = millis();
  static int deciSeconds = 0;
  
  if (millis() >= timer) {
    deciSeconds++; // 100 milliSeconds is equal to 1 deciSecond
    timer += 100; 
    if (deciSeconds == 10000) { // Reset to 0 after counting for 1000 seconds.
      deciSeconds=0;
    }
    sevseg1.setNumber(deciSeconds, 1);
    sevseg2.setNumber(deciSeconds, 1);
  }

  sevseg1.refreshDisplay(); // Must run repeatedly
  sevseg2.refreshDisplay(); // Must run repeatedly
}

First of all, you have a while(true) in your loop, that makes no sense. The loop already loops for ever.

You are also changing the number every time the loop() is run, making it flicker. If you follow the Arduino library example, you can see they only use setNumber every so often and use refreshDisplay every time the code runs through the loop().

Also, you didn't setBrightness, which shouldn't be a problem since the library probably sets a default value, but I'd advise on including it in your code to eliminate unforeseen problems.

Try this code and let me know if it works:

#include "SevSeg.h"

SevSeg sevseg1; //Instantiate a seven segment controller object
SevSeg sevseg2;

void setup() {
  byte numDigits = 4;
  byte digitPins1[] = {2, 3, 4, 5};
  byte segmentPins1[] = {6, 7, 8, 9, 10, 11, 12, 13};
  byte digitPins2[] = {14, 15, 16};
  byte segmentPins2[] = {17, 18, 19, 20, 21, 22, 23, 24};

  sevseg1.begin(COMMON_ANODE, numDigits, digitPins1, segmentPins1);
  sevseg1.setBrightness(90);

  sevseg2.begin(COMMON_ANODE, numDigits, digitPins2, segmentPins2);
  sevseg2.setBrightness(90);
}

void loop() {
  static unsigned long timer = millis();
  static int deciSeconds = 0;
  
  if (millis() >= timer) {
    deciSeconds++; // 100 milliSeconds is equal to 1 deciSecond
    timer += 100; 
    if (deciSeconds == 10000) { // Reset to 0 after counting for 1000 seconds.
      deciSeconds=0;
    }
    sevseg1.setNumber(deciSeconds, 1);
    sevseg2.setNumber(deciSeconds, 1);
  }

  sevseg1.refreshDisplay(); // Must run repeatedly
  sevseg2.refreshDisplay(); // Must run repeatedly
}

I did not take a look at the library you are using (sevseg), but I do see you are refreshing your display in your loop. You do realise this loop runs really fast. More like extremely fast. The code might take a few milliseconds (1 / 1000th of a second) to communicate to the seven segment display what segments should be turned on and off. But right after that, you do the same thing again without waiting, let's say 1000 milliseconds.

So what this does is it makes the Arduino tell the seven segment display what number to show (making it refresh it's LED's) and then it tells the display to show a new number (might be the same number), still it refreshes the display again. And again. And again.

The microprocessor can do this sooooo fast that we will see this as a flicker and not really see what the display is supposed to display.

(Also, you loop already loops. Having a while (true) in your loop makes no sense like that.)

Try this code and let me know if it works:

#include "SevSeg.h"

SevSeg sevseg1; //Instantiate a seven segment controller object
SevSeg sevseg2;

void setup() {
  byte numDigits = 4;
  byte digitPins1[] = {2, 3, 4, 5};
  byte segmentPins1[] = {6, 7, 8, 9, 10, 11, 12, 13};
  byte digitPins2[] = {14, 15, 16};
  byte segmentPins2[] = {17, 18, 19, 20, 21, 22, 23, 24};

  sevseg1.begin(COMMON_ANODE, numDigits, digitPins1, segmentPins1);
  sevseg1.setBrightness(90);

  sevseg2.begin(COMMON_ANODE, numDigits, digitPins2, segmentPins2);
  sevseg2.setBrightness(90);
}

void loop() {
  static unsigned long timer = millis();
  static int deciSeconds = 0;
  
  if (millis() >= timer) {
    deciSeconds++; // 100 milliSeconds is equal to 1 deciSecond
    timer += 100; 
    if (deciSeconds == 10000) { // Reset to 0 after counting for 1000 seconds.
      deciSeconds=0;
    }
    sevseg1.setNumber(deciSeconds, 1);
    sevseg2.setNumber(deciSeconds, 1);
  }

  sevseg1.refreshDisplay(); // Must run repeatedly
  sevseg2.refreshDisplay(); // Must run repeatedly
}