You're right - there isn't any link between BLM and trans.
But TRAs cynically FORCED a link. As soon as BLM became a thing, in summer 2020, #blacktranslivesmatter began trending, and Black Trans Lives Matter posters were seen on marches, and the woker end of the influencer/celeb spectrum adopted this as a talking point.
There was a big TRA tlaking point at the time, and I apologise in advance for offending anyone by reminding you, but the TRAs were saying that Black women weren't historically seen as women, but more like men. Therefore, the argument went, if you don't see transwomen as women, then you also don't see Black women as women. Therefore, unless you support trans rights, you are racist.
Can you imagine anything more racist and disgusting than that! But it was a HUGE talking point online in 2020 - 2021. TRAs were cynically piggybacking off of a real movement and using it for their own ends, just like PIE did with the gay rights movement in the 1970s.
When I saw this disgusting argument being made, I decided to read up the original sources from antebellum slave traders in the Deep South, and the language used in Jim Crow, to see if the racist power structures of the time did, indeed, see Black women as quasi-men. And guess what? I couldn't find anything. Even in the most dehumanising language used by slave traders in advertising their 'wares' in advance of slave markets, they still describe their enslaved Black women in traditionally sexist feminine terms - in terms of their reproductive ability, their skills at housework, caring for children, needlework etc. So I'd like to see where the TRAs got this horrible racist idea from. Because they never post any sources for their claim.
Anyway, don't listen to me - visit Lipstick Alley, the world's biggest website run by Black women for Black women. See what they've got to say about the TRA idea that Black women and transwomen are somehow equivalent. Prepare yourself for some....very forthright views.
In fact, read Lipstick Alley on TRA matters in general. This is a demographic which saw the truth far earlier than we did, and weren't shy of expressing it, either.