I'm so sorry, and I can understand your anxiety.
However you are not just a passive recipient of healthcare, you have agency over what investigations you consent to, and I personally wouldn't have an invasive procedure without a face to face appointment with a consultant in which they would have to convince me why it was really, really necessary and why for example a borderline endometrial thickness and a bit of spotting in someone with no risk factors for endometrial pathology (if that's true) cannot be monitored with a further scan in 3-6 months.
How much leverage you have also depends on whether you are taking HRT or not, which you have not mentioned.
If you aren't on estrogen then there is no risk of your prescription being weaponised to coerce you to have the biopsy.
Less than 1% of endometrial biopsies are positive for malignant changes, and whilst any medical procedure is an individual decision, I personally would have a much higher threshold for undergoing an endometrial biopsy.