The rookie pool is $9.7 million but the actual cap space required is a calculation based on adjusting that pool total by a dollar amount (league minimum which is $705K in 2022) times the number of picks a team has. Over the Cap had the effective cap space required estimates and had the Cowboys at $3.5 million or so.
The logic behind that calculation is that the draft picks take the place of people already on the roster who are eating up cap space. So while the rookie pool is $9.7 million, those drafts picks could/would likely replace 9 guys counting against the the Top 51 in the cap making near league minimum and ergo, the team would only need to account for an additional $3.5 million or so.
In other words, it would cost the Cowboys $3.5 million more to add all 9 draft picks and replace 9 people counting against the cap already.