Looking at his post, the main criticism is "that the program has not yet generated anything new", but the post does not refer to the actual results (like formulas for Catalan's and Apery's constants).
The two blog posts by Frank Calegari are from July 2019 and irrelevant to the paper in Nature (from February 2021). The paper went through peer review by mathematicians and experts in the field.
His criticism was discussed and found incorrect by the peer review process:
https://static-content.springer.com/esm/art%3A10.1038%2Fs415...