You are correct, deaths lag a bit, as does reporting of the deaths, which downward biases the IFR. Antibodies also lag before they show up in the serology tests, which upward biases the IFR.

But broadly, the studies I've cited largely back up the CDC's estimate of 0.4% IFR. Some of them have methodology in the papers themselves which give similar numbers, and I encourage you to read the raw data.

But an IFR close to the flu is not at all surprising. Covid is a respiratory infection. It kills the same way the flu kills (eg. pneumonia), so you'd naively expect them to have similar fatality rates and outcomes, and they do.