Ghrelin (hunger hormone) has strong anti-inflammatory properties which might be why you feel so hungry. Your body might be attempting to lower inflammation. Grhelin also has antidepressant actions which also sounds like another problem you are having.
Your primary problem is not SIBO. Your problem lies in your stomach and that is what needs to be treated. Could you have an ulcer? Any H. Pylori test?
When stomach function is compromised, SIBO can occur because stomach acid does help keep the small intestine clear of bacteria. It might be an issue but it is not causative IMO. If you get your stomach working as it should, any problems with SIBO will be rectified.
A stomach acid test might be worth doing. It's not highly accurate but it might indicate if there is a problem. It's very inexpensive just using Sodium Bicarb.
Your protein digestion is likely to be affected which might be causing an amino acid deficiency, especially the detox and anti-inflammatory amino acids such as cysteine, glycine and glutamic acid/glutamine which are needed for Glutathione. Glycine does increase GABA levels so can cause calmness and even sleep. It seems a bit counterproductive with fatigue but it is needed in quite large amounts. The body does manufacturer some but additional in the diet can be helpful to reduce the load on the liver. Some amino acids stimulate GABA production whereas others are more stimulating which can balance the effects of GABA. Glutamic Acid when converted to glutamate is stimulating on the brain and nervous system. I mix glutamic acid with magnesium carbonate to produce magnesium glutamate. Upto 1.5ml at a time of Glutamic acid converted to glutamate is okay but any more than that hurts my head. I adjust it according to what other amino acids I consume.
You are almost certain to have Increased Digestive Permeability which is likely to be where the inflammation is coming from caused by immune system reactions to absorbed large food molecules.
This is where the brain fog comes from. This is causing extreme stress on your liver due to the very high detox demands that your liver has. Nutrient exhaustion is common in these cases. Your body will use every nutrient it can get to support liver function. This often causes constipation due to acetylcholine deficiency because the liver is using all choline for other more essential uses. Your difficulties your liver is facing is contributing to your mood/depression.
BTW do not waste time and money on Leaky Gut cures because none of them work because none of them treat the infection which causes it. Lesky Gut is a false term because the digestive system has to be leaky or everyone would perish of malnutrition. It is Increased Permeability which causes problems allowing larger food molecules to enter the blood stream which causes problems with the immune system and liver. Waste products from the gut are also absorbed into the blood stream adding to the problems.