There are actually two variables that drive this behavior.
You tried the first one,
lsp-enable-snippet and it didn't work. This means that the culprit is probably
company-lsp, which engages in a similar behavior and uses a variable that is nearly identical,
Try disabling that with
(setq company-lsp-enable-snippet nil) and see if that does the trick 🙂.
As an aside, when I struggle with a problem like this (where I have a suspicion there is a tangential/related mode driving the behavior), I try to looking for similarly named variables or variables that contain a reference to the behavior/feature/setting at hand. It's not a perfect heuristic, but it is how I found out about company's complementing behavior to lsp mode as answer above. If you have a feeling a problem is of this nature, next time try using
C-h v and searching for the culprit variable.