You've made a couple fundamental missteps in your research.
1) Never rely on a single dictionary to confirm your suspicions about a word. A single dictionary definition can rarely capture all nuances of a word. From Wordnik:
publication (noun) An issue of printed or electronic matter, such as a book or magazine, offered for distribution or sale.
2) I would argue that the Lexico entry does support your initial hunch. After all, it says:
publication (noun) A book or journal issued for public sale.
but if we look up journal on the same website, we find:
journal (noun) A newspaper or magazine that deals with a particular subject or professional activity.
So, if you wanted an umbrella term for newspapers and magazines, I'd argue that you could use publications. If you wanted the term to include news websites, you might be able to use news journals as well.