I am new to php, but in other web technologies, you can share objects between page instances. For example, in java jsp pages you easily have on class that exist as static cl
Most of the PHP database libraries use connection pooling already. You call, for example, pg_connect as if you were requesting a new connection, but if the connection string is the same as a connection that already exists, you will get the established connection back instead. If you only care about pooling for database access, then you can just confirm that it exists in the db library you're using.