Brahmanas, Kshatriyas, and Vaishyas are called the twice-born. Their
first births take place when they are delivered of their mother's womb
; their second, when they duly accept the Gayatri Mantra from their
preceptors (21).
Thus made twice-born, and free from all other faults, they become
entitled to study the Vedas, Smritis and Puranas (22).
Vyasa Smriti verses
Verse 21 says that Upanayana (where one duly accepts the Gayatri mantra from their preceptors) is like the 2nd birth for the twice-born persons.
And, verse 22 says that only after Upanyana a twice-born becomes qualified to read not only the Vedas but also the Smritis and the Puranas.
So, by vedas, did lord shiva mean only the Rig, yajur, sama, atharva ,
or everything including the derivatives like the scriptures, geetas,
upanishads, purans etc?
By Vedas, Puranas, Gitas are not meant. Vedas primarily mean Vedic Samhitas. Some people say that Samhitas+Brahmanas=Vedas. Some other says that Upnaishad and Aranayakas are also part of Vedas.
But, regardless of such difference of opinions, Gitas and Puranas are not part of Vedas.
But, still the Vyasa Smriti is stating that Upanayana is the purificatory ritual that makes one qualified to read the scriptures like Gita and Puranas.