The 'two truths' in Pali Buddhism are different to the 'two truths' in Mahayana Buddhism. Possibly, the 'two truths' of Mahayana Buddhism are more relevant to Plato's Parmenides.
In Pali Buddhism, the 'two truths' refers to the difference between how enlightened & unenlightened people interpret certain (mundane/moral) teachings of the Buddha, as follows:
The Awakened One, best of speakers, Spoke two kinds of truths: The conventional and the ultimate. A third truth does not obtain.
Therein: The speech wherewith the world converses is true, on account of its being agreed upon by the world. The speech which
describes what is ultimate is also true, through characterizing
dhammas as they really are.
Therefore, being skilled in common usage, false speech does not arise in the Teacher, who is Lord of the World, when he speaks
according to conventions.
Commentary by Buddhaghosa
In Pali Buddhism, the translations "being" ('bhava') and "non-being" ('vibhava') refer to two kinds of dependently originated 'becoming' ('bhava') based on two kinds of dependently originated craving (as defined in the 2nd noble truth in SN 56.11), namely, 'bhavatanha' (craving to be) and 'vibhavatanha' (craving not to be). Both kinds of craving & becoming involve 'self-view'.
In other words, 'non-being' is not synonymous with the enlightened or unconditioned state of selflessness/emptiness (sunnata).
Some relevant texts that show how the translations 'being' & 'non-being' are used are below:
Idaṃ kho pana, bhikkhave, dukkhasamudayaṃ ariyasaccaṃ—yāyaṃ taṇhā ponobbhavikā nandirāgasahagatā tatratatrābhinandinī,
seyyathidaṃ—kāmataṇhā, bhavataṇhā, vibhavataṇhā
Now this, bhikkhus, is the noble truth of the origin of suffering: it is this craving which leads to renewed existence/becoming (bhava), accompanied by
delight and lust, seeking delight here and there; that is, craving for
sensual pleasures, craving for existence, craving for
extermination. SN 56.11
~~
So neva taṃ abhisaṅkharoti, na abhisañcetayati bhavāya vā vibhavāya vā. So anabhisaṅkharonto anabhisañcetayantoanabhisañcetayanto: ? bhavāya vā
vibhavāya vā na kiñci loke upādiyati, anupādiyaṃ na paritassati, aparitassaṃ paccattaṃyeva parinibbāyati. ‘Khīṇā jāti, vusitaṃ
brahmacariyaṃ, kataṃ karaṇīyaṃ, nāparaṃ itthattāyā’ti pajānāti.
He does not form any condition or generate any volition tending towards either being or non-being. Since he does not form any
condition or generate any volition tending towards either being or
non-being, he does not cling to anything in this world. When he does
not cling, he is not agitated. When he is not agitated, he personally
attains Nibbāna. He understands thus: ‘Birth is destroyed, the holy
life has been lived, what had to be done has been done, there is no
more coming to any state of being.’ MN 140
~~~
sato vā pana sattassa ucchedaṃ vināsaṃ vibhavaṃ paññapenti
Those who describe the...extermination of an existing being (satta)...Just as a dog, tied by a
leash to a post or stake, keeps running around and circling around
that very post or stake, through fear of identity and disgust with identity keep
running & circling around that same identity... MN 102
'Samsara' is defined as the state of the mind circling & running around in ignorance & craving:
From an inconstruable beginning comes samsara. A beginning point is not evident, although beings hindered by ignorance and fettered by
craving are running around & wandering on....Just as a dog, tied by a
leash to a post or stake, keeps running around and circling around
that very post or stake; in the same way, an uninstructed,
run-of-the-mill person...keeps running around and circling around that
very form... that very feeling... that very perception... those very
fabrications... that very consciousness. He is not set loose from
form, not set loose from feeling... from perception... from
fabrications... not set loose from consciousness...
SN 22.99
Therefore, dependently originated "being" and "non-being", namely, wanting to be this & not wanting to be that, are certainly characteristics of 'samsara' & probably reinforce each other.
However, whether they relate to Plato's Parmenides is another matter.