Try going just low carb for a few weeks (50-100 g) and see how you feel. Then if you wish just push the carb level lower bit by bit over the course of several months and keep track of any changes.
https://ketosummit.com/can-keto-cause-adrenal-fatigue/
https://virtahealth.com/blog/sodium-nutritional-ketosis-keto-flu-adrenal-function

I have slight hypothyroidism - I take 30 mg dessicated thyroid and that works perfectly for me whether on keto or low carb.

As always, check with your trusted health provider. Only you and they will know best.

The best thing for adrenal fatigue is licorice root (in the absence of hypertension) or nervous fatigue...

Keto would be good for adrenal fatigue because it's a cortisol lowering diet. Meat/veg and whole grains are recommended for adrenal fatigue, and processed foods should be avoided, this is also very close to a keto diet if you limit the quantity of grains. 50g of carbs is a pretty standard start for keto levels and still leaves room for a lot of vegetables and some grains.

Thyroid issues depend a lot on what the root issue is - something autoimmune would be helped by keto, while something like an iodine deficiency would be helped by lots of shellfish and lugol iodine. Selenium rich foods like eggs, fish, and nuts if it's a deficiency there.

I'm reading a book called In the Flo that sounds like right up your alley. Discusses adrenal fatigue and diet at length. Although she's not personally keto, she addresses keto and understands that people are choosing it for health reasons and you can follow her plan while remaining keto or low carb. https://intheflobook.com/