WASHINGTON — President Joe Biden has been quickly thrown into a high-wire balancing act with Russia as he seeks to toughen his administration’s stance against Vladimir Putin while preserving room for diplomacy in a post-Donald Trump era. The relationship is sure to be different from the one Putin enjoyed with Trump, who was enamored of the Russian leader and sought his approval, casting doubt on Russian interference in the 2016 elections and involvement in a massive hack last year.