You should take those headlines with a grain of salt because they grossly misrepresent the studies they are reporting on. Quoting directly from your article:

"The median 401(k) balance is just $35,345."

Most people who have a 401(k) work at more than one company in their career and rarely roll funds over into the new company's 401(k). It's more common to leave it or roll it into an IRA.

All we know is the median 401(k) account balance at Vanguard is $35k. Vanguard doesn't know about these people's other retirement accounts at Fidelity or Schwab or wherever. If their customers hold IRAs at Vanguard, those aren't accounted for. In the case that a person has multiple 401(k) accounts with Vanguard, it wasn't even clear if the account balances are summed together and counted as one account.

tl;dr These reports are always about average and median retirement account balances, which is not at all the same as average and median retirement savings.