With a working menus system, the first thing to add is a clock.

If possible, I don't want to add a RTC chip, so I have to find a way to get time.

Fortunately, we have NTP / Network Time Protocol. So I only need a working internet connectivity to set time.

Here is the piece of code to do just that :

unsigned int localPort = 2390;      // local port to listen for UDP packets

/* Don't hardwire the IP address or we won't get the benefits of the pool.
 *  Lookup the IP address for the host name instead */
// IPAddress timeServer(129, 6, 15, 28); // time.nist.gov NTP server
IPAddress timeServerIP; // time.nist.gov NTP server address

const int NTP_PACKET_SIZE = 48; // NTP time stamp is in the first 48 bytes of the message

byte packetBuffer[ NTP_PACKET_SIZE]; //buffer to hold incoming and outgoing packets

// A UDP instance to let us send and receive packets over UDP
WiFiUDP udp;

unsigned long sendNTPpacket(IPAddress& address)
{
  Serial.println("sending NTP packet...");
  // set all bytes in the buffer to 0
  memset(packetBuffer, 0, NTP_PACKET_SIZE);
  // Initialize values needed to form NTP request
  // (see URL above for details on the packets)
  packetBuffer[0] = 0b11100011;   // LI, Version, Mode
  packetBuffer[1] = 0;     // Stratum, or type of clock
  packetBuffer[2] = 6;     // Polling Interval
  packetBuffer[3] = 0xEC;  // Peer Clock Precision
  // 8 bytes of zero for Root Delay & Root Dispersion
  packetBuffer[12]  = 49;
  packetBuffer[13]  = 0x4E;
  packetBuffer[14]  = 49;
  packetBuffer[15]  = 52;

  // all NTP fields have been given values, now
  // you can send a packet requesting a timestamp:
  udp.beginPacket(address, 123); //NTP requests are to port 123
  udp.write(packetBuffer, NTP_PACKET_SIZE);
  udp.endPacket();
}

void get_NTP() {
  Serial.print("Starting UDP\n");
  udp.begin(localPort);
  Serial.print("Local port: ");
  Serial.println(udp.localPort());
  
  //get a random server from the pool
  WiFi.hostByName(ntpServerName, timeServerIP);

  sendNTPpacket(timeServerIP); // send an NTP packet to a time server
  // wait to see if a reply is available
  delay(1000);

  int cb = udp.parsePacket();
  if (!cb) {
    Serial.print(".");
  }
  else {
    Serial.println("");
    Serial.print("packet received, length=");
    Serial.println(cb);
    // We've received a packet, read the data from it
    udp.read(packetBuffer, NTP_PACKET_SIZE); // read the packet into the buffer

    //the timestamp starts at byte 40 of the received packet and is four bytes,
    // or two words, long. First, esxtract the two words:

    unsigned long highWord = word(packetBuffer[40], packetBuffer[41]);
    unsigned long lowWord = word(packetBuffer[42], packetBuffer[43]);
    // combine the four bytes (two words) into a long integer
    // this is NTP time (seconds since Jan 1 1900):
    unsigned long secsSince1900 = highWord << 16 | lowWord;
    Serial.print("Seconds since 1 1 1900 = " );
    Serial.println(secsSince1900);

    // now convert NTP time into everyday time:
    Serial.print("Unix time = ");
    // Unix time starts on Jan 1 1970. In seconds, that's 2208988800:
    const unsigned long seventyYears = 2208988800UL;
    // subtract seventy years:
    unsigned long epoch = secsSince1900 - seventyYears + timeZone * SECS_PER_HOUR;
    // print Unix time:
    Serial.println(epoch);
    setTime(epoch); 
  }    
}

get_NTP()

Conversion from epoch to human time is easily done with the TimeLib library. For an example :

String timeNow = String(hour()) + ":" + String(minute()) + ":" + String(second());

Finally, here is the piece of code I'm using to display the analog clock :

int screenW = 128;
int screenH = 64;
int clockCenterX = screenW/2;
int clockCenterY = ((screenH-16)/2)+16;   // top yellow part is 16 px height
int clockRadius = 23;

void analogClockFrame(SSD1306 *display, SSD1306UiState* state, int16_t x, int16_t y) {
  ui.disableIndicator();

  // Draw the clock face
  //  display->drawCircle(clockCenterX + x, clockCenterY + y, clockRadius);
  display->drawCircle(clockCenterX + x, clockCenterY + y, 2);
  //
  //hour ticks
  for( int z=0; z < 360;z= z + 30 ){
  //Begin at 0° and stop at 360°
    float angle = z ;
    angle = ( angle / 57.29577951 ) ; //Convert degrees to radians
    int x2 = ( clockCenterX + ( sin(angle) * clockRadius ) );
    int y2 = ( clockCenterY - ( cos(angle) * clockRadius ) );
    int x3 = ( clockCenterX + ( sin(angle) * ( clockRadius - ( clockRadius / 8 ) ) ) );
    int y3 = ( clockCenterY - ( cos(angle) * ( clockRadius - ( clockRadius / 8 ) ) ) );
    display->drawLine( x2 + x , y2 + y , x3 + x , y3 + y);
  }
  
  // display second hand
  float angle = second() * 6 ;
  angle = ( angle / 57.29577951 ) ; //Convert degrees to radians  
  int x3 = ( clockCenterX + ( sin(angle) * ( clockRadius - ( clockRadius / 5 ) ) ) );
  int y3 = ( clockCenterY - ( cos(angle) * ( clockRadius - ( clockRadius / 5 ) ) ) );
  display->drawLine( clockCenterX + x , clockCenterY + y , x3 + x , y3 + y);
  //
  // display minute hand
  angle = minute() * 6 ;
  angle = ( angle / 57.29577951 ) ; //Convert degrees to radians  
  x3 = ( clockCenterX + ( sin(angle) * ( clockRadius - ( clockRadius / 4 ) ) ) );
  y3 = ( clockCenterY - ( cos(angle) * ( clockRadius - ( clockRadius / 4 ) ) ) );
  display->drawLine( clockCenterX + x , clockCenterY + y , x3 + x , y3 + y);
  //
  // display hour hand
  angle = hour() * 30 + int( ( minute() / 12 ) * 6 )   ;
  angle = ( angle / 57.29577951 ) ; //Convert degrees to radians  
  x3 = ( clockCenterX + ( sin(angle) * ( clockRadius - ( clockRadius / 2 ) ) ) );
  y3 = ( clockCenterY - ( cos(angle) * ( clockRadius - ( clockRadius / 2 ) ) ) );
  display->drawLine( clockCenterX + x , clockCenterY + y , x3 + x , y3 + y);
}

Disclaimer : this is part of the clock demo I added to the SSD1306 lib, here : https://github.com/CaptainStouf/esp8266-oled-ssd1306/blob/dev-branch-3.0.0/examples/SSD1306ClockDemo/SSD1306ClockDemo.ino