I felt something like that affect, though not very pronounced, for the first couple weeks. Since then I've felt completely normal. Life is way more fun now.
Sounds quite a bit like when I started the probiotics I've been on for quite a few many years now: When I started these ones, I actually started feeling worse than before. Ultimately though, after IIRC about two weeks of feeling worse than before, things got better.
I started out being lethargic all the time (in hindsight: way, way too many years, I just didn't put 2+2 together on multiple symptoms!). Migraine headaches from certain foods as well as any amount of alcohol and even non-alcoholic beer for example, essentially anything that produces histamines (which certain foods as well as alcohol consumption does).
After the probiotics "fought and won the battle" against whatever was inhabiting my intestines before that, I felt totally fine. No more lethargy. Could eat all the histamine rich foods in the world (Roquefort, here I come again, you're soooo tasty! Maybe with a glass of red wine too) and be fine. Never looked back. Life is way more fun now.
I might want to get on GLP-1s to not like alcohol and too much Roquefort now, while still not being lethargic, lol!
So I am a lot more picky about side effects than I would be if I seriously needed to lose weight or had diabetes.
But my BMI was like 39, and now it is ~25. My blood test results the last couple of years have been phenomenal. All of the extra cardiac testing I've done suggests I managed to dodge a lot of the effects of being obese, which is just genetic luck (heart disease does not run in my family, most of my immediate ancestors lived well into their 90s and all of them died of something other than heart disease, even though some were fairly overweight).
I have played a little roulette with GLP-1s lately because I am curious, and found that at my current weight (5'11" or so and 175lb) seems to be where my body is willing to go, and that's about it. I stalled out pretty abruptly, and if I increase the dose all I get are uncomfortable side effects and no real weight loss -- even though the discomfort pushes my caloric intake well into the "cannot get enough vitamins and minerals" level. It's remarkable. I was once 165 naturally but 30 years ago, and that just isn't a realistic goal any more, so says my body. This is fine, I feel very good now. Well, when I'm on the maintenance dose ;-). Then I have no side effects, I just live a normal life eating normal amounts of healthy food and having a way easier time exercising than when I was heavy.
I forgot about sleep apnea. I was struggling with adjusting to CPAP, and never really succeeded. After losing a fair amount using tirzepatide, I did a repeat sleep test and my sleep doc gave me the green light to put the CPAP in storage.
I was beating my head against those sleep issues for years, and had multiple doctors sit down and tell me that I probably "just had a high sleep need." In the end, I'm not sure whether it was the thyroid or some vitamin deficiency (before the multivitamin I was on iron, C, and D separately), but it turned out to be very treatable.
If you’d lost the weight without GLP-1s, your blood test results would still have been phenomenal. Most of the effect you are seeing is the result of lowered bodyfat% through calorie deficit.
now, in your case calorie deficit comes from GLP1 use but in others case it can come from sustainable dieting which is little more tricky execute properly than just injecting a drug.
I've lost the weight several times over the last 30 years. The test results were never so dramatically improved. Your hypothesis may be wrong.