Does VACUUM FULL need ANALYZE
The statistics are produced from the values in the columns. As these values are not changed by VACUUM FULL or even by VACUUM, a fresh ANALYZE is not specifically required.

If the database is in a maintenance window, it's a good opportunity to run it, though. Its execution time is likely to be insignificant compared to VACUUM FULL.

By default, a DBA will rely on autovacuum/auto-analyze rather that doing this manually, with the exception of the manual ANALYZE for when a new table that was just bulk-loaded or heavily modified is immediately involved in a query for which a good planning can't be obtained without good statistics.