Here's a simplification (that I experienced before I dealt with cfs) -
there is long series of stairways up a large hill that people run up.
You can run up the hill slowly every 5th day without it killing you, then every 4th,3rd 2nd then everyday. That process might take 4-6 months and takes grit.
Or you can strength train your legs with barbell squats once a a week for 8 weeks noticing yourself getting stronger each week and then just run up the hill.
I accept I'm a terrible athlete now so I strength train my legs with very amateurish pistol squats so I can walk up the hill without crossing over the lactate threshold.
If you are crossing the lactate threshold lifting a kettle then strength training should help. I know the exact feeling you are describing and used to deal with it. Gradual strengthening helped - with a strong emphasis on the gradual. Aim for fragmented single limb swimmers stretches. I still remember the pure exhaustion after doing 1 rep. Make sure your body has glucose before after and during any form of exertion. The steadier the glucose flow the better. Getting up and down off the floor is a form of strength training.
There's a balance between strength and endurance and I don't have the explanation off the top of my head but exercise physioloogists do.
Zone 2 exercise heals mitochondria. Zone 3 exercise stresses it and requires a recovery period. Exercise physiologists are having good success treating cfs as athletes are really just optimising their mitochondria so they can thrash it harder and longer than their competitors on race day. Exercise physiologists often work in with physio teams at sports academies at univerisities.
Dr Peter Attias stuff he is figuring out and sharing from helping wealthy intelligent people live long debilitation free lives is very useful for understanding lactate thresholds.
Just like athletes take performance enhancing drugs to reduce recovery times - so can we. There are plenty of supplements to play around with. So many people mess up their B vitamins by taking multi-vitamins but getting b vitamins in quanties your body is utilising is a low hanging fruit. Unfortunately it has no profit motive attached to it so you have to guess or work with a Complementary Medicine MD if you can afford one. A low inflammation, glucose goddess style diet with moderate cheating in the mix so you don't get food obsessed as the base helps also.
The supplement reccommendation page on www.perfecthealthdiet.com is a safe base to play around from for supplementation. If you adapt a soft version of the perfect health base diet to the glucose goddess method and gradually strength train I think you must increase the probability of escaping the fatigue trap. Some of it is mental but if you can get small wins you eventually beat the mental side back as well. Dopamine managment is a factor.
My frustration with some medical professions take is that they sometimes expect you to deal with it purely via mental resilience (which helps) without providing any tools to get any small wins which is impossible. If you think about it - an olympic athlete has a coaching team to ascend mount everest, what do we have?
The medical system treats the condition like someone's on a cave dive and provides the support encouragement, training and advice afforded Eric the eel. They are right that you can do it, panick won't help and that you do need to keep moving in some direction but until you run out of air you will be alright. The fact you can't work is irrelevant, lot's of people deal with debilitation. From the health systems perspective maybe they are right - who deserves saving vs who deserves training are different questions. There is alot of suffering out there - maybe placing the onus on the individual to figure their own path is the correct approach.