if you quote someone in-text, and acknowledge the name and page number but accidentally leave them out of your works cited page, is that plagiarism? will it be treated severely?

So you are saying that you added the citation but not the reference? If so, it should simply be considered a correction.

I quoted an indirect source ie X claimed in 1932 that "...." (quoted in W, p96). But W is missing from my works cited page.

Plagiarism is attempting to pass off someone else's work as your own. You haven't done that here - agree it would be a correction.

Thanks guys.