Is it true that there were only 350 Ashkenazi Jews about 600-800 years ago?

I have seen this claim multiple times on Jewish tik tok recently. The claim is that 600-800 years ago, there were only 350 Ashkenazi Jews left in Europe, and that all of us today are descended from this group. I looked it up (cursory google search) and all the top results are articles about a genetic study that supposedly confirms that claim.

But that makes no sense as far as I can tell. 1200-1400 was a significant time period in Jewish history. If this fact were true, that would mean the well-poisoning accusations, which happened throughout Europe during the black death, were directed at a whole of 350 people. Some of the expulsions that happened between the 13th-15th centuries would have had to have been expulsions of tiny amounts of people if this were true. This just seems like such an unlikely claim.

Have you all heard of these studies before? Do they have any merit? Is the information simply being twisted by the articles for shock value?