I feel that it doesn't make much sense for it to not be common knowledge, atleast among people on the grand line where Devil Fruits are pretty common among people whose profession involves danger of death all the time. I mean, it's not shown, but people die all the time off panel. And normal fruits are fairly commonplace, since their importance was directly stated in order to prevent scurvy back at the start of OP.
So, whenever a devil fruit user died, either a fruit that bestowed those same powers or at least someone with those same powers would shortly show up in the vicinity atleast somewhat often. Enough to establish a pattern that when devil fruit users die, their powers in some way resurface in that area. Without even being scientific about it, it's just something people would notice.
Someone who has a penchant for killing and fine food like Bege does, he'd probably be one of the more likely to notice that a devil fruit suddenly showed up in his cargo hold when he Sonny'd some poor dude.
I don't think Caesar's experiments would have been possible if it went into any random fruit in the world. The reason Caesar was okay with killing off his smiley is because he knew he wouldn't risk losing the fruit he imbued him with once he did.
