The Fed doesn't set bond interest rates. Rates on bonds are set by an auction. If bond interest rates are low, it's because bond investors want bonds. Which is to say, they think the US government will have no trouble paying them back. So the government borrows cheaply, and investors believe they will be able to continue to.

The Fed sets a different rate, one that banks use to lend money to each other. It forms kind of a floor for lending. They raise it to reduce lending, and thus slowing down the economy in general (and thus reducing inflation).

They've kept the latter at nearly zero -- arguably for the not-great reason of propping up assets. If anything, raising that would make bonds more attractive relative to stocks, dropping the interest rate further. Instead, we've gotten inflation, but only in the asset markets, not consumer inflation.

They actually wanted consumer inflation to be higher, so that consumers would be forced to put their money in asset markets rather than holding it in cash. They've finally gotten their wish, though it's likely that it is due more to pandemic-related shutdowns than to monetary-based demand.