See
https://www.newsweek.com/biden-adopts-sanders-agenda-itemsheres-where-he-aligns-left-1517078
The cost of Sanders' Medicare for All was computed last spring when Sanders was still a candidate. Several think tanks costed.
When Biden sewed up the Democrat nomination, he adopted most of Sanders' platform and AOC's Green New Deal.
"A government run health care system . . ." is code for Medicare for All.