The food grade buckets are either HDPE (High Density Polyethylene) and PET - Polyethylene terephthalate.
Both materials are FDA approved for use in food storage.
HDPE and PET are not manufactured with any BPA. (which is often in polycarbonate and listed in those articles above). Many polycarbonates (Nalgene type bottles, Camelback bottles) are now not being made with BPA either.
There are some catalyst agents like Antimony that may exist in the finished product of PET, in trace amounts.
The studies that do exist often just show that there may be chemicals present, but don't actually go into the full on health effects. Many studies are flawed, biased, and with limited statistical support evident. Here's one link.
https://www.sciencedirect.com/science/article/pii/S0045653520319275
I could pull more.
I spent most of last year at work solving an issue with polyamines hydrolysing polycarbonate causing BPA to leach from the material. This had nothing to do with food grade material but on medical grade material. I successfully solved and resolved the issue.
I'm not remotely worried about my plastic buckets.