For what it's worth, it may be a regional thing, but in Monterey, California, we had a very big sardine industry not long ago. Sardines were produced in the canneries on a street called Cannery Row. This was made famous in 1945 in the John Steinbeck novel by the same name: Cannery Row, and later in 1982 in the movie by the same name.
Sardines are canned in canneries using a process called canning, and you generally won't find the word tin mentioned anywhere. (source: The little fish that we can: California’s sardine industry, now and then)
Online stores in Monterey call the containers cans, as this picture shows (although the single cans seem to be unavailable, they can be bought in a twelve pack).
The American company Walmart describes their sardine products as being sold in a can:
If I look on Amazon.com, the suppliers describe their products both ways, with can being preferred only slightly, if it's mentioned at all. This surprises me, because I can't recall ever having heard anyone refer to a sardine tin in the United States (except maybe my wife's grandmother, but she was from Bermuda).
Since the Ngram Viewer is popular here, I've run one on AE usage, and then BE usage. There is definitely a preference inversion in the corresponding literature. But this distinction is stronger in AE, going for can, not tin:
One more thing I forgot to address is your question about BPA-free containers. I think you will still find them called cans, as in this article, 7 Companies You Can Trust to Use BPA-Free Cans, which never mentions tin as what the BPA-free containers use, nor do they call the containers tins. Yet they still achieve BPA-free results for their products.