As of yesterday (5/2) afternoon, any free agents signed by NFL teams no longer count against team’s compensatory pick count. Prior to the draft, Overthecap.com (who seems to be the gold standard on this topic (and several others)) had the Commanders at two compensatory picks in the 2023 draft.
The comp pick capital was gained by having Brandon Scherff and Tim Settle walk in free agency for contracts that were sufficiently large - $16.5M and $4.5M, respectively - that they met the compensatory pick cut off threshold. DeAndre Carter, who signed a $1.14M/yr contract, was not sufficiently highly compensated to qualify.