Master's thesis, should I inform my supervisor about the mistake? Please hear me out first,

I am one week away from submitting a manuscript, the deadline is in one week.
The supervisor has reviewed my thesis and is happy with my results.
He is writing a paper based on my work.

Now I used a technique in my work that is fairly different is almost never used, but it yielded good results so I went on. I told my supervisor during earlier days that I using that technique and he said it's not the norm, but whatever you do just document it. He never questioned my decision or said it doesn't work.
Fast forward 13 months, and I've come to know that you are not supposed to use that technique as it introduces some bias in the results, which is not discernable.
Now I am more than willing to inform my supervisor, but this will have a domino effect and I might have to start my experiments again, which will take more than one and a half months at least, and I have been working on my thesis for 18 months now.
Why should I not tell my supervisor:

He has reviewed my thesis and he is happy with my results.
My student visa expires in 21 days, and another thesis extension (if it happens) with the university would be whole another hassle, and I am not sure if I will even get the extension.
No money to pay the rent. this is a big one, up to this point I have survived by a very little margin, with no funding from the department, and I have no work now, another one and a half months would mean at least 70K $ which I cannot arrange.
Visiting parents after 2 years of not going back home because of masters, and short on money.
18 months of already working on a thesis, having done my very best, I am f****ng tired now. I just want to hand in the thesis and sleep in peace. Every single student in my class has given their defense I am the only one left.
I want to move forward with my life, get engaged and find a job. 4 years of master's school, with zero
funding from my department, even when they were happy with my work.
Getting rid of my supervisor for good, he was always pushing me and
pushing me, and I worked my ass for this thesis without any returns.
Not dealing with him would be the highlight of the year for me.
It is a 100+ page thesis, from a different perspective, it shouldn't
nullify all of my work.
I can always plead ignorance in the end. Since I am not from a
computer science background, this thesis is at the CS department
though, they know I am always learning or whatnot.
I can defend it, my supervisor is one of my graders, and he is on my
side.

Why should I tell my supervisor:

It's eating me up from inside. It is my baby, my work, I've put 18
months of work into it. It only deserves to be 100%
My supervisor is writing a paper that he wants to submit to Nature
based on my results, and it has that faulty method I used. This kills
me.
I feel like a fraudster/criminal.
Scared my work will be thesis work might get canceled in the future.

I would be happy if you can help me solve this quandary.
Everybody makes mistakes. What separates good researchers from poor ones, is how well we own up to them. I don't know the details of your work, but it is very possible that what you think is a devastating mistake, is an oversight which should simply be improved upon if the work is later submitted as a journal article. Note that it is very rare that a Masters thesis becomes a journal article unaltered.
You should get in touch with your supervisor and tell them that you have discovered this paper, which you think might be warning that your method is questionable under these specific circumstances. Then let your supervisor form their own opinion.