Tidal effects mostly transfers it to the moon, the sun has almost no tidal effects.

Tidal effects from the sun are about 46% as strong as those from the moon.

<https://oceanservice.noaa.gov/education/tutorial_tides/tides...>

Why would angular momentum be conserved? Rotation within an atmosphere should cause friction would should convert angular momentum into thermal loss.

Interestingly, it looks like the upper atmosphere generally rotates faster than the planet, so it could be that the opposite effect actually dominates. IE the uneven heating causes a atmospheric bulge that actually pushes the atmosphere around slightly faster than the planet rotates, thereby slightly contributing to planetary angular momentum.

Energy conservation and momentum conservation are different

Because the system exhibits rotational symmetry. It follows from Noether's theorem that angular momentum is conserved. Only when you include the interactions with other stellar bodies you lose the symmetry and you have an opportunity to shed angular momentum.

There is interaction with other stellar bodies. Massive and uneven amounts of thermal radiation from the sun. Black body radiation out.

Sure. I'm not going to perform the computation, but my physical intuition tells me that it's completely negligible. The amount of thermal energy the earth absorbs or emits per year must be dwarfed by several orders of magnitudes compared to the rotational energy or the energy lost via tidal friction.