SQL Server - Index Including PK
The clustered index key is included in every non-clustered index as the row identifier.

SQL Server just ignores an INCLUDE of the clustered index key.

If your PK index is NONCLUSTERED then it will not be included in every row of all other NC indexes.

You can test this yourself by making two identical indexes, one with INCLUDE(ClusterKey) and one without, and compare the sizes.  They will be identical, even on hundreds of millions of rows.