FYI:They can use any sterile tissue for growing a vaccine. Not sure why people might use human/fetal tissue, but maybe there's lots of it.
The cells are not used as a growing medium. They use fetal stem cells because they are a very simple cell that can be made to generate any of many kinds of cells.
When the president was treated for covid the researchers used stem cells to create a cell with spikes similar to the covid virus so they could test whether the experimental drug would bind to the spike on the virus. Of course they could have used real covid virus, but that would have been dangerous, even in a lab setting. By using stem cells that trained to mimic that one feature of the covid virus it greatly simplified protocols to keep it from escaping the lab or affecting researchers and enabled faster development.
The problem with stem cells is that they are only conveniently harvested from embryos. It is feared that this would make a market for fetuses and thus encourage abortions. So, as a compromise there are a relatively small number of stem cell strains from fetuses aborted years ago that may be used for research (at least in the USA).
It is unclear if they are used at all in the creation any of the vaccines, but I find that they always specify that no such cells are actually in the vaccines rather than say that stem cells are not used at all in their development a little ambiguous.