It's mostly known, but you're probably right it's not exactly known
45 trillion across all retirement accounts, 12 trillion in defined contribution (including 401k), 9 trillion in just 401k
https://www.ici.org/statistical-report/ret_25_q2
In that chart, the 18T of IRA has portion in private equity, and the 15T of pension (defined benefit) has a portion in private equity. The 13T defined contribution plans (of which the vast majority is 401k) can't be placed in private equity right now.