I also understand that there is currently no way to repair a unit's losses other than manually, though I am not sure doing that mechanically is even possible. Is this also correct?
Thankfully, version 1.12 of the game added a way to replenish troops.
Basically, in the ground unit screen, click on the fourth tab on the top, the Unit Series one.
How unit series work is you make a series for every element you want to be able to automatically replace (IE Infantry, Infantry with CAP, Infantry with LAV, etc). Then, if a unit does not have enough of an element compared to the template it was based on, it will take elements from units marked with the "replacements" checkbox.
Example: I have a formation (call it formation A) that has used up some of its supply trucks. I go to the unit series page, and create a new series called "supply truck", and add my supply truck element to that series. Now, I can mark another formation (Call it Formation B) to be used for replacements, and so Formation A will automatically take supply trucks from Formation B until the number of supply trucks in it match the number of supply trucks that it had when built.
Note: If a unit is marked to be used for replacements, it will not be able to then be able to automatically replenish itself.
Note 2: you can put more than 1 element in a unit series. The unit on top will be used to replace losses from any of the units in the series.