I definitely do avoid exercise due to negative emotions... although for me it's moreso a barrier to actually getting started than it is to continuing on with the exercise. During these times I try to go for low-barrier-to-entry exercises, ie, running is a good one even though it's hard on your joints. If you just get your trainers on or whatever and step outside your front door... then for me I'm committed and that's enough. It often does suck - but I'm usually able to push through and just keep on going, even if I cut short my planned route now and then.
Actually I find weight training harder to stick with during times I'm not feeling psychologically well. Part of this I think is that there is too much time to think. Unlike cardio where it's almost meditative - or at least, I find it so - especially if you focus on keeping your breathing regular, ie, breath through your nose throughout, don't start panting with your mouth open, just breath in, breath out, really focus on the sensations, your pounding heart, how much it sucks, and realise all of this is just another object in consciousness... an illusion. Generally that occupies my mind enough that I can avoid thinking about quitting too much.
With weights on the other hand... it's a lot of slow controlled movements, rest periods, etc, a lot of opportunity to think and for your mind to wander... and I find this a struggle at times. Additionally if I'm feeling really socially anxious and avoidant the prospect of going to the gym even is offputting. If you have this problem I'd try to go really early in the morning, if you have a 24 hour gym near you, go at night or like 4/5 AM. The one near me opened at 6 AM and that was the best, mostly empty, and also the few there are a good crowd I found, polite, respectful, obviously self-motivated types... no obnoxious screamers getting in the way and taking mirror selfies... lol, that's just my bitchiness talking though. During the pandemic I bought myself a basic home gym set-up but I have used it a lot less than I thought I would... somehow the fact that it's now RIGHT THERE means that the psychological effect of taking the first step, ie, getting your ass in the gym, is removed, and whereas before I'd be like damn, I better make this worth it, now I'm kinda like eh, I'll just do 1 set and carry on later...

The psychological barriers to consistent training are numerous...
I do and have used various chemical aids to keep myself motivated at times though, I've found low or even medium doses of benzos can be a training aid, for lifting anyway, as evidenced by day after DOMs. You would think the opposite due to the muscle relaxation effects but it seems to work for me. Phenibut is good too and probably a safer and more sustainable option - this also doesn't have the muscle relaxation effects and potentially might even help with GH release... Caffeine obviously is an age-old exercise enhancer, although not everyone finds that actually motivating to get yourself moving in the first place. Other stimulants can help, phenylpiracetam, modafinil, that's as hard as I would go personally, I've worked out on amphetamine but I think this is asking for trouble, overtraining and injuries. In general I would not advise taking drugs too often to train but since you ask about a low dose of benzos... I would say yet it can be effective. But just to get the ball rolling or get yourself out of a funk. Not all the time.
Additionally - I would say with exercise, perfect is very much the enemy of good, and it took me a long time to figure this out. During periods of laziness, or when I've planned to work out super early the day before, but then don't, or am planning to work out later, but later never comes, my thoughts are usually something like, "I'm gonna do a
proper workout soon, so no point exercising just yet, I should conserve my energy"... But this is an unhelpful thought. Just do little exercises when you think of it, when you've been sitting down too long, if you're feeling like shit, thinking about when you're gonna work out... just do some pushups. Do some bodyweight squats. Do some pullups if you have a pullup bar/station (and if you don't I'd strongly recommend you get one). Just do one set and then chill. Or if that feels good, do a few sets, do a little circuit. But just one set is fine. Then maybe do that again an hour later. Recently I thought I'd just do 15 pushups every hour for a while because I wasn't doing any exercise and was feeling like a lazy shite (someone else told me about this thing, the pushup challenge, do your maximum - mine was 30 - then do half of that every hour for a week - I wasn't that strict about it, but, damn, it's better than nothing!).
So yeah, just do little things. You don't need to commit to a proper 30-60 minute session, and the thought of committing to this can be daunting. But every little helps. Also if you can exercise first thing in the morning - for me that's ideal, although I do not do it every day, and I don't do a big workout, just like 5-10 minutes of body-weight stuff to wake myself up and before I've had time to think or make excuses. Again - I don't do it every day - sometimes I give up halfway through - sometimes I'm a lazy fucker for weeks. But, perfect is the enemy of good. When you think about it - do it. Do some pushups after reading this post!
Finally - and I'm always banging on about this - I think doing exercise classes can be really helpful because then there's social pressure to push through the discomfort. It doesn't really matter what type of class, just as long as you have someone giving instructions, other people doing it around you, and that you'll feel worse just publicly giving up than you do forcing yourself to continue. Again I always suggest this but martial arts are a great one for this. But anything works, any skill you might like to have. Maybe you'd like to get better at handstands? Try finding a handstand class.
If all of that is even too much you can start with low intensity physical movement, just try to commit to some stretching, yoga is great and there's a bunch of videos on YouTube, but just work on your flexibility for a few minutes a day, 10 minutes if you can. It's low impact, and it's good for you and will help you to start getting into a fitness mindset. Yoga can be pretty punishing I will say but you don't have to start with the punishing stuff, just work on getting more flexible maybe. I decided recently I'd commit to doing split-stretching for at least 10 minutes a day with the goal of being able to do the full splits at some point... I can't yet lol, I don't do it every day, but again, perfect is the enemy of good and it's just a way to keep my head in the game of taking care of my physical fitness in some small way no matter what that is.
I hope some of that helps! Excuse the wall of text, but, it's an interesting question I think and turns out I have a lot of thoughts on it, I guess because I also have had to practice a lot of psychological tricks to keep myself in good shape despite my tendencies to just slack at everything in my life.
EDIT: Oh! One other thing I've just remembered, substance wise. I have used NSI-189 on and off and have found to have some quite strange effects, one of them being that it seems to really reduce exercise-related feelings of stress, possibly also fatigue although I'm not sure it has any real effect on performance. It's also surprisingly very helpful for crushing stimulant comedowns in terms of normalising soul-deep regret and anxiety. Sober, it's effects are pretty minimal, maybe it does something, but it's a weird substance with a somewhat unknown mechanism of action that stimulates neurogenesis in the hippocampus, so was under research for treatment of depression, and hypothesised to reverse stress-induced hippocampal injury (hippocampal atrophy is a known physical result of extreme stress and trauma, especially those that experienced this at a young age). I believe it failed to meet the Phase 3 endpoints so research was discontinued but in actual fact it showed interesting benefits in the first 2 Phases and you can find various tidbits from these studies online - it just didn't meet the previously decided objectives to be a marketable product, as I understand it.
One mechanism by which it is theorised to work (or so I've heard/read) is that it blocks cortisol release, and this would correlate with the subjective impact on exercise-induced stress, and stimulant comedowns, which perhaps have vaguely overlapping neurological profiles even if they are very different in other ways. So you might want to give this a try - and it may well be a far better option than benzos or probably any other "harder" performance aid which may not help your ability to unlearn this stress reaction to exercise.
The only other thing to bear in mind is that some other substances I believe you have shared you take often may interfere somehow - for example, a few people have reported ketamine and NSI-189 do not mix well and I have found this to be true of other NMDA-antagonists as well... the effect was not terrible, but it was also not pleasant, and I have no idea if it correlates to any negative brain changes or if it interferes with any of the positive ones... in fact no-one really does, but, it's just a point of caution to bear in mind.