Maybe it could be easier to consider for the start unpowered flight.
For a glider, the best glide AoA and best glide L/D and IAS should be independent of density and TAS - so long as the TAS remains low in terms of Mach number.
For any given air density, there should be some AoA, IAS and TAS, lower than the best glide AoA, where the sink rate is slowest. The slowest sink IAS and TAS should be slower than the best glide speed.
As the glider flies higher, its L/D, best glide IAS and slowest sink IAS should stay unchanged. But its best glide TAS, slowest sink TAS and slowest sink rate should increase with decreasing density.
How does existence of engines change this?