Database storage limit for open source PostgresSQL
On their webpage About they clarify that the limit is a lot huge than 4GB.

Limit        Value

Maximum      Database Size  Unlimited

Maximum      Table Size 32 TB

Maximum      Row Size   1.6 TB

Maximum      Field Size 1 GB

Maximum      Rows per Table Unlimited

Maximum      Columns per Table  250 - 1600 depending on column types

Maximum      Indexes per Table  Unlimited