Mode S & ADSB are not the same thing.
In what is called a Professional Pilots Network, there seems to be a huge gap in the general understanding of ModeS and ADSB and Flight Radar 24.
ModeS is a transponder system like ModeC, except that in addition to displaying altitude, it displays a unique id number for the Transponder. All Mode C transponders look the same to the receivers, and depend on the selected Squawk to make a difference obvious when you see two of them on the screen. Radar systems can not tell the difference between two Mode C aircraft squawking the same code.
ADSB is a different thing entirely. It runs in the background and is carried by the Mode S squawk.
In simple terms;
Mode A sends a four digit 0-7 code.
Mode C accompanies that ModeA code with the altitude of the aircraft, based on 1013.
Mode S has the A & C data and adds in a unique ID for that airframe.
ADSB is tagged on to Mode S and sends the GPS derived Lat/Long of the aircraft and some other details, like heading, speed, call-sign, route and others.
That's it simplified just enough to suit the needs of this forum.
As for FR24, ADSB Exchange, or better still 360Radar.co.uk tracking them, they have different filters in place, depending on what they have agreed with aircraft owners.
FR24 do not show some airframes, Military and Police are usually missing, despite having ADSB on some.
360Radar show all that they receive, no filtering, and their display includes Police, Military, Coastguard, Private aircraft and SAR resources such as lifeboats.
For an ADSB equipped aircraft, the tracking sites mentioned, only need one receiver, out of the thousands that they have all over the world, to pick up the transmission from the aircraft, and that's what allows the public to see it on the web page.
For an aircraft with Mode S without ADSB, the sites all need 5 ground station receivers to get the response to an SSR Radar head pinging the aircraft. The 5 or more stations, send the received data to a server that crunches the time difference between each response, related to the exact location and height of the receiver's antenna, and plots a position for the aircraft. This process is called MLAT. The results of this are added to the ADSB results and makes a composite page where lots of aircraft show up, some ADSB and some just Mode S that have been subject of MLAT calculations.
So... if you only have Mode C, they know you are out there, but can't plot a position for you, as you don't have an ID attached to the squawk, so the server that crunches the number can't be sure of the responses coming from just one aircraft.
Even if you have Mode S, they need 5 hits on each pulse, to be sure of your position.
So even if this aircraft had been transmitting Mode S, it might still not have been within range of enough FR24 receivers to get MLAT'd so it will not be on their page. No conspiracy theory, no non-squawking skullduggery, just the wrong part of the world. 360Radar.co.uk do not have enough contributors in that neck of the woods to be confident of seeing cross channel traffic at that height. FR24 might be in the same position, as lots of contributors feed more than one system.
The total costs, for the end user to monitor Secondary Radar in this way, come to less than £100 as a one off. You buy a small device (Raspberry Pi, or use an old PC) and connect it to a cheap mast, on the chimney or in the loft, and using your domestic broadband, you send away to the server, all that it hears.
In exchange for sending your reception up, they give you access to the shared product of all the calculated positions resulting from you and many others sending in data. There are thousands of "anoraks" all over the UK doing this. Alliances are being formed world wide, and in the next 12 months, an almost complete coverage of the globe is to be expected.