Holding the health of their leaders close to the chest has been the way Russian authorities and its media have handled things since the early 20th century. The only post-monarchy leader whose health was regularly spoken about publicly was Vladimir Lenin, who came to power after the fall of the Czars.
Putin initially became Russia's acting president after serving as prime minister under the leadership of Boris Yeltsin. The country's Constitution states that the same situation would occur if Putin died while still in office. But, it's unlikely that a transition of power to Prime Minister Mikhail Mishustin would be peaceful.
With a background in taxes, Russian Prime Minister Mikhail Mishustin is a technocrat, which means he is an expert in his field but not a career politician. Before being named prime minister in 2020 following Dmitry Medvedev's resignation, Mishustin "worked in tax collection" and eventually "headed the Federal Tax Service”.
Having undone much of what former President Boris Yeltsin did to build up the country's democratic systems, Putin has made himself a "new" kind of Russian "tsar," according to Michael Rubin. In 2014, Vyacheslav Volodin, Putin’s former deputy chief of staff, said “There is no Russia today if there is no Putin”.