At least twice (on the comments of this answer, and mentioned in passing on this book), I have read that the moon takes energy from Earth due to tidal drag. The notion seems that: a) energy must conserve, b) if the Moon exerts tidal force on Earth, Earth must exerts reaction force on the Moon, and c) Earth loses energy due to tidal force, then, we can conclude that the Moon must gain the same amount of energy due to reaction force. This is what I suppose by taking quite a big reasoning leap, which I don't understand and doesn't sound plausible at all.
There is a similar argument made by this answer, which seems equally unappealing. I mean, angular momentum must conserve, but it doesn't necessarily have to go to the Moon.
I always had the impression that most of the spinning energy lost by Earth due to tidal forces (and the same happened to any tidally locked planet) is lost via viscous dissipation (heat, ultimately) on the fluids dislodged by the tidal force (atmosphere, oceans and, mostly, the liquid core (which also loses energy through the magnetic field it generates)).
The problem of conservation of angular momentum can be solved the same way as with any fluid vortex dissipated via turbulence: it is transferred to the smaller scales vortexes down to individual molecules, which on the average of the total rotation, they cancel out.
So, the question is, is there any meaningful amount of energy transferred from Earth to Moon due to tidal forces? How it affects Moon movement (or shape)? How this process works, exactly?