The earliest mention of the four speech levels I found in the Rig Veda (1.164.45):
च॒त्वारि॒ वाक्परि॑मिता प॒दानि॒ तानि॑ विदुर्ब्राह्म॒णा ये म॑नी॒षिणः॑॥
गुहा॒ त्रीणि॒ निहि॑ता॒ नेङ्ग्॑यन्ति तु॒रीयं॑ वा॒चो म॑नु॒ष्या वदन्ति॥ ४५॥
catvāri vāk parimitā padāni tāni viduḥ brāhmaṇā ye manīṣiṇaḥ।
guhā trīṇi nihitā neṅgayanti turīyaṃ vāco manuṣyā vadanti ॥ 45 ॥
Speech is divided into four categories; they are known by the wise brāhmaṇās.
Three of them are hidden, and the fourth category is spoken by ordinary people.
Yāska, in his Nirukta, gives other interpretations of this śloka – he does not link them to the four forms of vāk(c), which are popular in Vedanta, Tantrism and Nātha yoga, but of course, not everything has to do with his Nirukta. Basically, in terms of meaning, I think that there is the form of speech, which can be heard by everyone and the other three are at the level of manas (madhyamā), buddhi (the awakened “seeing” consciousness of paśyantī). The level of parā is Brahman himself. Parā is not a manifested creative vibration or logos, but it is a creation in the form of a seed in its potential, the latent one. We could call it the primordial Parabrahman, who is not manifested and from whom we are not initially separated. Further, it manifests itself in the form of its free will (svatantriya), in the likeness of a flash of light (sphoṭa) and the spontaneous expansion of the sound (anāhata), that is a natural expression of the will (icchā) of the Absolute, who is Śabda-brahman. This level is called paśyantī (seer). It should be clarified here, that unlike parā, we, as the ones who are seeing, are not separable from the object of our vision, i.e. there is nothing separate from us, but in the case of paśyantī, a separation of the object from the subject (us, as Absolute) already appears. Although, even when there is a separation, our expression is still conditionally separated from us. After that, the logos itself reveals its purpose in the form of the archetypal image of our consciousness, which still exists at the stage between the physical and the subtle levels. Therefore, it is called madhyamā (the middle). Then, we “express our thought” – this is vaikharī (physical level). To make it easier to understand, we can correlate vaikharī with kriyā, madhyamā with jñāna and paśyantī with icchā, and parā is the unity of Atman and Paramātmā (Brahman), Śiva and Śakti.