There are money market funds which only invest in US govt debt, e.g VMFXC which yields 4.23%.
investor.vanguard.com - Mutual funds ...
investor.vanguard.com - Investment products

But read your links.

The first one isn't a pile of T-bills.
About a third of the fund is repo agreements. Another third is not in T-bills but in "US government obligations", which generally allows inclusion of agency securities which do not have the stated guarantee of the US government, but merely assumed to behave as if they do. Plus of course there are certain layers of risk introduced merely by the fact that it's a fund.

The second fund is allowed to have up to 20% in stuff other than T-bills, provided management thinks they have "economic characteristics that are substantially identical", and "may also invest in debt securities that are not included in the Index, cash and cash equivalents, or money market instruments, such as repurchase agreements and money market funds (including money market funds advised by the advisor)."

These are better than some, but money market funds are generally sausages trying to look like meat.

If you want the safety of T-bills, buy T-bills. Or if you're taking on various additional risks, be aware that you are doing so.

Jim