How can I get prescribed sleeping pills?

I don’t want to say anything that gives them increased reason to just dismiss me or act like I’m making things up/exaggerating

This seems to be an excuse, not a reason. None of your posts suggest realistic engagement with going to your GP at all to me, and gave proved your adept at avoiding any kind of oversight if you wish by simply going to different sources for what you're seeking. So even if we take your objection at face value it's clearly not an issue because you could and, based on the information provided, would change GP if you didn't think you were getting what you wanted.
So clearly you would have nothing to lose by going to the GP - except perhaps actually having the underlying issues treated and no longer having the crutch of those.

Lorazepam or diazepam

I’ve never asked for medications by name so I would try anything they would be willing to prescribe to me

When you read the NHS webpages for Lorazepam, Diazepam, Zopiclone, what were your take-aways?
In terms of information that's relevant to you? Inparticular, anything that stands out as a big warning as to why you shouldn't be prescribed any of these?

If a doctor will prescribe them to me, it’s my own decision whether I want to take them and with what

And can you see any reasons on the website that indicate why, so far, no doctor has prescribed them for you?

No

Therein lies the problem.

The problem is that I go to my doctors repeatedly and explain what problems I’m having and always just get sent away without them even wanting to investigate what it could be and just telling me that “that’s just how it is for some people”.

Zopiclone:
https://www.nhs.uk/medicines/zopiclone/about-zopiclone/
It's usually prescribed for just 2 to 4 weeks. This is because your body gets used to it quickly and after this time it's unlikely to have the same effect. Your body can also become dependent on it.
So lets say - purely as a thought experiment - that you somehow manage to get prescribed zopiclone and you somehow manage to stay alive for the 4 weeks that you take it. What happens after that?
Do not drink alcohol while you're on zopiclone. Having them together can make you go into a deep sleep where you find it difficult to wake up.
Who do we know that's currently drinking 8 units of alcohol per day?
Zopiclone is not suitable for some people. To make sure it's safe for you, tell your doctor if you:

Speak to your doctor or pharmacist before starting to take zopiclone if you take any of these medicines:
strong painkillers such as codeine, methadone, morphine, oxycodone, pethidine or tramadol
So, codeine, alcohol, zopiclone as a daily cocktail? NO!

what's stopping you from registering with another practice if you feel like you aren't being taken seriously in your current one?

Hence why I haven’t told my doctor how much I drink or that I’m taking the painkillers

That still leaves the big question of what would happen at the end of the 4 weeks when your prescription would end?
It's a Catch 22.
If it's chronic, giving you a prescription for a drug that will provide relief for 4 weeks is not the answer.
If it's a new sleep issue then it wouldn't warrant the drastic step of prescribing you medication that could lead to premature death. Because their approach would be to wait and see if it resolves itself, or if you can resolve it by applying the sleep rules.
On top of that, there may be something about you that makes them suspect, or even know that you consume codeine and alcohol.

"Crap" when it comes to what you're eating and drinking is all relative and depending on context.
Given that you have acute and chronic stomach pains, headaches and sleep patterns, what you consumed the other day left a huge amount of room for improvement. As discussed in post 25 above.
Was that day fairly typical for you? Or was it one of 2 days per year that you drank alcohol (eg your birthday and xmas)?
The mentality that so many people have is that they have self destructive lifestyles - with the self destruction being of various degrees. And they then look to the NHS to bail them out and fix them.
There's also a lot of people that have the self image that they eat healthily when they are in fact prodding risk factors for ill health and premature death.
5 a day is a rather dumbed down target because so many people eat so badly in the UK and the advisors that come up with these guidelines realise what an uphill struggle they have to get people off their junk and semi-junk food and drink diets.
A good target is 50 different plants eaten per week.
Another is to eat sufficient fibre that your stools are soft and come out without straining. And that it takes about 24 hours (or less) for your food to pass through you, which can be checked by eating beetroot and looking for pink on your toilet paper.
Another good target is to not get stomach aches. To feel fine inside - relaxed and comfortable. To feel like you have bright eyes instead of stingy / fatigued eyes.
You being a regular drinker that consumes painkillers would be relevant to your sleep issues, stomach aches, headaches.
Have you tried applying ALL the sleep rules discussed in page 1 of this thread? Consistently for at least a month?
It's worth repeating that it's not only the addictiveness of sleeping pills, it's the risk of premature death. When they work no better than cognitive behavioural therapy in the form of being taught the sleep rules.
Do you have any health issues apart from the sleep?
What exactly did you eat and drink yesterday?

for me im vegetarian most my life i normally eat toast/pasta a lot and ive tried literally everything and nothing helps me sleep better 😭

Exactly, people are so quick to come out with **** about constantly eating crap as if I (and most other people with health issues) don’t eat healthier than the majority of people

There is very little nutritional value in what you have described. Sure, it's better than you previous diet of Greggs and energy drinks and alcohol, but it's by no means a healthy and balanced diet so stop deluding yourself.

I’ve never been overweight in my life, compared to the average modern person who has a bmi of 27.5. And my doctor has said that my diet is healthy

Not being overweight does not automatically equal being healthy. And most doctors know **** all about nutrition - according to this study, a large majority get less than 2 hours of teaching on nutrition as part of their training and only 26% feel confident in their nutrition knowledge.