We don’t really know - you are right to ask this question. There are two methods and they disagree with each other. JWST is precise enough to rule out a simple reason like instrument imprecision.
So remaining possibilities are new physics, a deep flaw in our assumptions/methods, or a universe which is not uniform (but in a peculiar way).
Perhaps the small anisotropy that is observed in cosmic microwave background observations imprints to the dark energy that accelerates expansion. I haven't kept up on the modern state of the art.
Becky Smethurst, an astrophysicist, goes through how the cosmic distance ladder works and the recent JWST results here[1].
As you say, measurement errors of Cepheid stars has been something scientists considered a possibility, hence why they're cross-checking by measuring them in different ways.
And, as mentioned in the posted article and the other papers mentioned in the video, it seems that measurement errors are very unlikely to be the culprit.
Preprints to the articles Becky mentions are here[2][3][4].
I've found this interesting and have read up a little on it. I believe there have been a good amount of studies trying to verify the different measurement methods. I believe they have made some progress in verifying the methods but I'm sure there is still more work to do. I think this is mainly in attempts to deal with the "cosmological crisis."
- On the one hand, the universe can be expanding at different rates.
- On the other hand, is it possible our approach to measuring the expansion (e.g., using Cepheid variable stars) might be the problem?