Thanks Alberto,
Yes granting solves it -- I was initially worried that that would mean overly broad permissions (as the warning box states here) but I guess it is moderately comforting to read:
Privileges on the ANY FILE securable cannot override Unity Catalog privileges and do not grant or expand privileges on data objects governed by Unity Catalog. Some drivers and custom-installed libraries might compromise user isolation by storing data of all users in one common temp directory.
https://docs.databricks.com/aws/en/data-governance/table-acls/any-file#privileges-for-any-file
In any case, another workaround remains for non-admin users to use classic compute for this.
(It is not in the same region, but I did not worry too much about region as they can read via classic already..)