Basic rocket science principles therefore suggest that you cannot bring enough fuel with you for any space trip except putting a satellite in orbit.
Basic common sense suggests that smaller payloads require less fuel to put into orbit. Do you agree with that statement?
Yes - pls study my website about it.
Good. Then would you agree that if you use a booster designed for a larger payload (let's say, 22,800kg) to launch a smaller payload instead (maybe 9600kg), then you could have some fuel left over that you could then use for recovery?
Yes. Problem is of course how to convert that fuel into a force to assist recovery. The force must be applied in the right direction at the right location/time/duration, etc, etc. and as you are moving really fast all the time it is difficult ... or, IMO impossible. Compare Apollo 11. So they fake it.
Yes it's hard. Hard is not the same as impossible and you have shown no reason why its impossible. You didn't even understand that they didn't have to add more fuel to the rocket for recovery flights compared to expendable until i pointed they out to you.
Of course they have to add plenty fuel to the rocket to enable recovery ... so the rocket becomes much more heavy at departure.
No. The rocket is fueled up as if it was going to deliver a 22,800 kg payload but it's only carrying a 9600 kg payload, so the weight at departure is actually 13,200 kg lighter at departure than if it was fully loaded.
But it does not help them. All is fantasy! The fuel must be converted to forces...
Yes, that's what they have rocket engines for.

... and the forces must be applied in the right directions at the right times, etc, etc. ...
Yes, that's why they have triple redundant flight computers and inertial guidance with a GPS overlay.
... and it is not possible.
Eight successful landings would seem to suggest otherwise.
Particularly not by Mr. Le On Ksum who is a big joke. Not even fun.
*sniff* *sniff* Do I detect the faint odor of jealously? What's wrong, is competition from SpaceX affecting the value of your Arianespace stocks?
Why do you insist the opposite?
Because the available evidence says that you are wrong.