I already knew In Opus, the setting you want is Hide file extension in Filename column, on the Display tab of the Folder Options or Folder Format editor:
In Details mode, it will keep the extension hidden (unless you do something like push Ctrl-E to select the extension part, which will reveal it).
Looks like you're using List mode from the screenshot, which doesn't do the same thing. I've made a note to check if that's intentional (maybe because there's no possibility for a Type of Extension column in List mode) or can be changed.