Primo
While it doesn't include everything ZSR offers, this is a good place to start. Choose different limits depending on your needs, e.g. "Peer Reviewed Journals," "Newspaper Articles," or "Videos." Limits by Date and Language are also helpful.
New York Times, Wall Street Journal, and other newspapers where you might need a special account.
Search Primo for newspapers.
World Newspapers
In English. Organized by country, so easier to find a Russian or Ukrainian perspective on the news.
Watch out for variant spellings (or variant transliterations) of names of people, places etc.
Examples: Kiev/Kyiv, Saint Petersburg/Leningrad
Use a * to cut off a word at its stem, e.g. Tolsto* will retrieve Tolstoy, Tolstoi.
In the library catalog, personal names have an official transliteration determined by the Library of Congress. Once you find one article about your person, you can use the author and/or subject links to find all the others.
Putin is Putin, Vladimir Vladimirovich, 1952-
If you can't use a star to search for spelling variants, use OR
"Saint Petersburg" OR "Leningrad"