Start with what 800 kcal a day leaves you room for, because at that intake the deficit is a live competing explanation rather than a footnote. Protein is 4 kcal per gram, so 100 g costs 400 kcal — 50 per cent of the entire day's energy — and everything else has to come out of the remaining 400. A day that misses protein at 800 kcal has missed it by a wide margin, and vomiting that tracks those days is a nutrition signal. Then separate the two by timing: a dose effect is periodic and phase-locked to the injection or to an increase, and a deficit effect is monotonic and gets worse the longer the intake stays at 800. Log intake, protein and vomiting on the same daily row for a fortnight and the two patterns separate without any further cleverness. Nothing here is medical advice.
Answer first: fatigue in this context is usually an energy-intake problem before it is a drug effect, and the arithmetic is the first place to look.
A deficit beyond about a thousand kilocalories a day reliably produces fatigue, reduced training performance and reduced spontaneous movement. With appetite suppressed, deficits of that size arrive by accident rather than by plan.
On the detail: hypothyroidism, sleep apnoea, depression and anaemia all present as fatigue and all become more likely rather than less in this population, so attribution to the compound should be a diagnosis of exclusion.
Sleep is a variable here too, and no amount of eating fixes sleep debt.