Qin Shihuang really found the elixir of immortality - but the price was the fate of the entire Qin Dynasty.
Xu Fu's journey to the East really found the "elixir of immortality", but it was not an elixir.
Rather, it was an "immortal formation" - the fate of the entire Qin Dynasty was sacrificed in exchange for the immortality of the First Emperor. After serving, the First Emperor gained power far beyond that of a mortal, but the Qin Dynasty quickly collapsed...