Earlier quoted context omitted.
There's two ways to lean left. Do some leftward leaning, or stand still while your reference point ("the right") leans away. I personally think both of these have happened. I bristle at the inference that only one of them is taking place.
Except evidence has shown the the left has moved further left than the right has moved right. Both have moved but the left has moved further left in the US.
That depends on all of the time frame (are you talking from the height of the mid-to-late-1990s “neoliberal consensus” where the DNC had shifted sharply right on economic issues compared to its previous positions, and when—due in part to the economic boom, broader in reach down the distributional ladder than subsequent expansions—racial issues were at a historically low salience, or some other time), and your political frame of reference (a fix set of policy stands defining degree of left/right-ness, or comparison to evolving global or developed-world standards), and what you are calling “the left” and “the right” that have moved (are you talking about the nth-percentile position in the electorate, are you talking the median position in each of the major parties [and, if so, are you looking at the party-in-the-electorate or the party-in-government], etc.)
And, as with most identity-charged issues, standard selection tends to be biased by the desired outcome (either directly and consciously, or because of worldview, e.g., a conservative will be biased toward the constant-policy rather than evolving-international-norms standard in measuring how far to the right or left things in the US are.)