I'm looking at https://www.postgresql.org/docs/current/sql-analyze.html, where it says “Without a table_and_columns list, ANALYZE processes every table and materialized view in the current database that the current user has permission to analyze.”.
I don’t believe there is a separate “analyze” permission, so which tables is this? Tables owned by the user? Ones where it can insert/update/delete? Ones where it can select?
Owners only - at least in previous releases. I don't recall whether the addition of new roles to cover subsets of administrative privileges ever was extended to cover vacuum/analyze but I do not think it has.