For those who are elderly or with chronic illness who are around or near the sarcopenic obesity category before losing weight , it is possible that the muscle loss from GLP's could be clinically significant. And sarcopenia is associated with increased mortality and is a serious issue in the elderly. There is a case for being very careful with GLP's in this group.
For every one else, muscle and other lean tissue loss from weight loss of any cause including GLP's is proportional to fat loss, and in virtually all situations results in substantially improved functional capacity. The muscles are a bit smaller, but not having to move so much mass makes an ever bigger difference to actual real world abilities, like getting up out of chairs or walking up an incline or stairs. And GLP drugs improve muscle quality, reducing intramuscular fat and improving muscle strength to mass ratio by about 6%. So in the real world I am not sure the muscle loss problem is really much of a real problem. If people are far more capable in doing everyday actions or exercising, then does the loss of muscle mass really matter.
As I lost weight I found that each extra 10 kilos I lost made a fairly big difference to my ability to walk up a hill. At 115kg I was puffing and had to stop several times over about a 20-30m vertical incline, and it was seriously hard work. Once I got to 90kg or so I did not need to stop but it was still work, and at 75kg it was not hard at all, despite a pretty major drop in my muscle mass.
The problem with drug therapies to improve muscle mass and function , is that there are still no current therapies that have been proven in clinical trials to improve muscle mass and functional capacity despite a large number of trials of a lot of different drugs over many years, mostly in the context of sarcopenia due to age or cancer. Some do improve muscle mass, which might be helpful in the context of obesity for metabolic reasons , but it would be better if it could be proven it improved muscle quality by showing performance gains.
Exercise obviously works, even in the worst case scenarios of cancer or age or losing weight, and increased protein intake can improve the amount of muscle a bit , and can reduce muscle loss during weight loss.
The only grey drug I know of with actual clinical trial evidence of being used with GLP's is ostarine, at low doses of 3mg it nearly abolished muscle loss with semaglutide induced weight loss. But this is a single small study, as far as I know it is not an approved drug for any purpose anywhere, can cause liver toxicity at higher doses, so it cannot be said for certain it cannot cause this at lower doses, and is only available in 25mg pills that are hard to find, and getting 3mg out of 25mg pills sounds like a bit of a pain. As far as I know it is still in development , so further studies are likely eventually.
The other ones in development are all antibody based aimed at inhibiting myostatin, so even though they sound promising , they are going to be expensive and not available from grey sources as antibody therapies are much harder to manufacture than peptides.
I guess replacement dose TRT is proven to be OK medically in the context of androgen deficiency in males, which is very common in obesity but availability and access is pretty variable. In Aus if you are obese in general the standard medical therapy is to advise weight loss , not replacement.
Which leaves the various different methods in use by the body building community , none of which are approved medical therapies for the purposes of maintaining or improving muscle mass. Which does not mean they do not work, it does mean they are not proven to be safe and there is no scientific evidence that the benefits outweigh the costs in adverse effects, and in many cases the long term adverse effects in humans are simply unknown as there have never been any long term tests and you have to guess what they might be based on animal or cell studies.
The closest to safe I guess would be tesamorelin which has had multiple clinical trials in HIV lipodystrophy, where it reduced visceral fat and did not have adverse effects on lipids or cardiovascular risk. Never tested in any other population, so you cannot say for sure it is safe in other contexts, but at least somewhere in the vicinity of safeish. But not safe enough for Doctors to consider prescribing it for other reasons.
The problem with most of these therapies is that they could easily modify long term cardiovascular ( or other ) risk in an adverse way, and detecting this is hard, requiring long term, large population studies which are expensive and are not going to be done as there is no straightforward business model to justify it, so that using those treatments to improve muscle could end up defeating or reducing the health benefits of GLP's and weight loss. Probably not , but if you have a heart attack or a cancer 10 or 20 years after using then you can never know if they contributed to it or not.