I think there are other factors to also consider, alongside the option of suspending your studies.
First and foremost, working 0.8x FTE while doing a part-time masters is almost certainly going to be extremely challenging to maintain. Remember that in general full time degrees expect similar time spent on them on average each week as a full time job. So if you're doing a part-time degree at 50% intensity, working more than ~20 hours a week on your part-time job is going to be very draining as you're basically working 1.3x FTE! So you're doing the equivalent of a full time job plus a second part-time job. That's hard to sustain long term for most people, and that's even before considering that degree study is often a lot more stressful than a typical job. So I think you really do need to think about whether you should or can scale back your hours a bit. Ultimately with that kind of work intensity I think it would be quite challenging to complete the part-time masters even with a good supervisor-supervisee relationship and without any mental health challenges underlying it.
Secondly this does not sound like a good supervisor-supervisee relationship which is a really big issue. While I do agree on the point that your part-time work (or rather, nearly full-time work while doing a part-time degree!) is very likely to be impacting things, if the communication has gotten to the point where you don't trust them to guide you through the course and they don't trust you to complete the work, and messages are getting ignored, that's really something that needs to be addressed - this would be the case even if you had a similar situation (for different reasons) while studying full time, I think. So this is something you may want to approach your SU or a personal tutor other than your supervisor about (I would probably recommend discussing with the former first, although if you have a personal tutor who isn't your supervisor that you trust then it may be also something to raise with them in parallel). There might be scope to change supervisor and still complete your masters while completing the same project, or if the project is directly tied to that supervisor you may need to rationally consider whether completing that project with that supervisor is practical - as even if the project is great, if the supervisor isn't it's going to drag everything down for you. Alternately it might be that if you and your supervisor can sit down, you can hash out how you will work through the project and come up with a plan that works for everyone. It sounds like that ship may have sailed based on what you have said, but it could be that in general you have a good relationship but it's just been strained on a couple of points.
The third part to consider then is your mental health background. This is definitely something you should discuss with your GP or specialist (if under a specialist) about how you are managing your condition and finding coping strategies etc. You also need to discuss your medication and that it's stopped and whether this is something that may need to be restarted, if you might need to trial a different medication, or if you want to focus on non-pharmacological treatment. However this is really the backbone of everything else and so if your mental health isn't stable and you don't have a consistent treatment/management plan for it with your doctor it's going to make dealing with the other bits impossible. Obviously the exact details of what has worked for you in the past, what hasn't, how you want to move forward with that are very individual so something you need to talk through with your GP. I think stopping psychiatric medication "cold turkey" can be very dangerous in a lot of cases so you might want to also talk about why you felt you had to go that route and if you were started on a different one, what plans you can put in place so if you do feel you need to stop taking it, you can do so in a safe and controlled way.
So this brings us to the possibility of suspending studies. This can be an extremely helpful option in some cases - however it really only works out well if the problems absolutely can be addressed within that period of suspending your studies. If you have a chronic health condition, then you need to consider if the issue is due to a short-term flare up, or a period of instability of your treatment which can be adjusted during that period, or if it's just that overall the chronic condition isn't conducive to the activities you are doing. In the former cases then taking that interruption of studies is very viable as an option. In the latter case I think you would need to think about whether you can "fortify" yourself suitably during that year to push through the remainder of them afterwards or not.
However, suspending your studies will not solve all problems. In terms of your workload, unless you can work that whole period without affecting your mental health recovery, in order to save money so that you can scale back your hours when you return, it may not change that underlying issue. So this is something you need to look at and plan ahead financially for, while also considering how working in that time may affect your recovery healthwise. The bigger problem that I don't think it will solve is the supervisor relationship. "Time apart" is probably not going to fix a supervisor relationship by itself, so if it isn't resolvable now it probably won't be after the time out. However, that time away from your studies may be enough time to make arrangements for moving to a new supervisor, or getting onboard a new project. Whether this is desirable for you is another matter entirely, so is really up to you.
In terms of the student finance/sponsorship picture, this is harder to say due to the sponsorship angle. For undergraduate study at least, interrupting your studies shouldn't in principle affect your finance unless you begin your interruption midway through the academic year. If you do it between years, then it's just a "gap" between starting the next lot of funding or not and so is usually not a problem (assuming you can financially support yourself). However if you're being sponsored by a company, you will need to check the details of their sponsorship and what their requirements are. They may require you to complete it within a certain timeframe which interrupting would preclude, they just might not agree to it, if your sponsorship is a contract than there may or may not be clauses related to this in that.
So, a fair few things to consider and work through, but probably best to take it one thing at a time. To start with, get your appointments with your GP, specialists, etc set up so you can get a plan in place for your treatment and mental health support. You may also want to approach your university about what support they can provide through e.g. any accessibility or mental health services they provide - your SU might be able to advise on these. Which brings us to the next thing, which is to get in touch with your SU to try and have a meeting about the supervisor issues and what their advice is on this. Even if they can't offer any formal advice they can offer informal support! From there you can see how you want to go with the supervisor matter. As that's going on, you'll need to start looking at the financial picture - both considering how you support yourself now and if you can do so while working fewer hours, and seeing what the situation is with your sponsorship. Your SU may be able to advise on that to some extent, particularly if there's a contract that can be reviewed; if you do have a contract then your local Citizen's Advice Bureau might be able to support you in understanding your rights within that.
Once you have your health in process with appointments set up, discusssions started etc, have been able to speak to someone (probably your SU, maybe a trusted personal tutor who isn't your supervisor; I would again recommend going SU first though) about the supervisor relationship, and having looked at the situation with your sponsorship and reflected on your financial situation beyond that with respect to work, you can then start putting the pieces of the puzzle together to see if they fit into the mould of taking an interruption/suspension of studies. If they do, then you can weigh up the options and see if that's something you want to do. If they don't, then depending on how they may or may not fit that you may want to consider if it may still be worth taking one anyway, even if it won't solve all problems, or if it is not going to resolve anything and if you need to look at more significant shifts.