The issue seems to be connected with some specific configurations – for the public buckets the issue not exists.
As publii.files.json stores only checksum I will consider to use the same ACLs as for other files so it will be possible to store it in the same way as other files. Also I will check if it is possible to use bucket default ACLs to avoid conflicts with bucket ACLs and these used by Publii during upload.
It should cover most of the cases.
At this moment the only temporary solution is to manually upload publii.files.json to avoid resync of all files. The fix will be available in ~2-3 weeks with Publii v.0.41 planned for mid of October 2022.