Plasma has a setting to synchronize selection and clipboard or something like that.

Not exactly. When you select a text and copy it, the two selections will end up containing the same text, but you can write to either selection without affecing the other by using an API, e.g. a website's "copy to clipboard" button, or xclip/wl-copy.

Clipboard managers with a history feature are an altogether different layer on top of the standard selections. Plasma's clipboard manager only cares about the clipboard selection, and even then, there are exceptions (e.g. copying a password for KeepassXC doesn't save it in the history).