Yes my fatigue was pretty severe.
The way out of it was to reduce blood sugar, and I did try exercise which may have helped but really the thing that did it was careful attention to what I was eating and regularly using a blood glucose meter.
Don't worry about thinking you're lazy. I've always been so active that I've 'got away with' being overweight for most of my life. My heaviest was 21.5 stone (many years ago now), and even then it was me dragging friends at work out to go walking and climbing. People may think that I 'gave in' last year and decided to sleep for 20 hours a day, but it hits you like a ton of bricks and it's very hard to escape from as you no doubt have found out yourself.
Now that I've 'escaped' from what felt like a pit of fatigue, I've found that I need to be very careful with exercise. I do a ton of walking especially at the weekends, easily clocking up 20 hours, but that can lead to (and requires, to do it comfortably / safely when in some of the more remote hills) eating a fair bit of food, and that raises my fasting levels, and I felt the tiredness creeping back in the last couple of months. I'm just getting on top of it now by paying close attention to what I eat again.
So if you find your new exercise group too draining, don't feel like you've failed even if you give it up. You can do just as well by sitting still and eating sensibly initially, then when you have been out of toxic blood glucose levels for a while and start to feel good, if there's anything active you enjoy then go for it, but always monitor your levels - they must come first.