In Early Buddhism, the term 'eternalism' refers the wrong view of a permanent 'self'. Refer to DN 1, which refers to continuation of a self after death; and refer SN 12.17 & SN 44.10, which simply refer to 'eternalism' as belief in a permanent self (unrelated to death).
Therein, bhikkhus, when those recluses and brahmins who are
eternalists proclaim on four grounds the self and the world to be
eternal... DN 1
Kassapa, if one thinks, ‘The one who acts is the same as the one who experiences the result,’ then one asserts with reference to one existing from the beginning: ‘Suffering is created by oneself.’ When one asserts thus, this amounts to eternalism. SN 12.17
In Early Buddhism, the term 'annihilationism' refers to the wrong view of a discontinued 'self'. Refer to DN 1, which refers to ending of a self at death; refer SN 12.17, which refers to 'annihilationism' as believing suffering is caused by others; and SN 44.10, which refers to 'annihilationism' as believing a self existed in the past but may not exist in the present.
Since this self, good sir, is annihilated and destroyed with the breakup of the body and does not exist after death, at this point the self is completely annihilated.’ In this way others proclaim the annihilation, destruction and extermination of an existent being. DN 1
But, Kassapa, if one thinks, ‘The one who acts is one, the one who experiences the result is another,’ then one asserts with reference to one stricken by feeling: ‘Suffering is created by another.’ When one asserts thus, this amounts to annihilationism. SN 12.17
this would have been siding with those ascetics and brahmins who are annihilationists...the wanderer Vacchagotta, already confused, would have fallen into even greater confusion, thinking, ‘It seems that the self I formerly had does not exist now.’ SN 44.10
The heretical ideas exclusively about 'eternalism' referring to an afterlife vs the 'annihilationism' referring to no afterlife are, again, created by Buddhaghosa (the author of the Visuddhimagga) in his Theravada Commentary on DN 1. The second commentator named Dhammapala corrected Buddhaghosa's heretical commentaries but the worship of Buddhaghosa in Theravada continued to prevail. In summary, in Early Buddhism, the terms 'eternalism' & 'annihilationism' refer to two types of 'self-view' rather than are conflicting doctrines about an 'afterlife'.
Therefore, the Buddha's own approach is not a form of eternalism or annihilationism because the Buddha taught the doctrine of not-self (anatta).
In Early Buddhism, the complete eradication of suffering is real or a Noble Truth; therefore possible. If there was no Nibbana (end of suffering), there would be no Buddha and no Buddhism.
If we come from another (worldly) religion, we should not believe there is any other religion that comes anywhere near Buddhism. The Buddha did not evangelise his supramundane doctrine of Nibbana because it is simply beyond the capacity of most people who naturally are guided by craving. Nibbana is a superhuman (atikkantamānusakena; uttari vā manussadhammā) attainment in Early Buddhism therefore not a subject for the common worldling (puthujjana). The Middle-Way essentially starts as a life of celibacy, which is the definition of one of the Right Actions of the Noble Eightfold Path. In other words, there is no goal in Early Buddhism of re-orienting the entire society. Re-orienting the entire society was a goal of Moses, for example, in the Old Testament. But we can see how, according to the Old Testament and according to their mode of living today, this goal of Moses failed. The Old Testament continually mentions how those people rebelled against the Torah & fell out of the covenant.
In summary, in Early Buddhism, the term 'The Middle Way' refers to:
A Path of practise avoiding sensual pleasures and self-torture (SN 56.11). It is a Path of happiness or bliss based in the development of meditation "jhana", which is a pleasure far superior to any type of sensual pleasure (AN 2.64-76; MN 75). The problem with sensual pleasures is their pleasure diminishes, causing a search for other sensual pleasures; plus they involve many dangers, sorrows & traumas (MN 54; MN 13; MN 14; MN 75; MN 22).
A Path of not viewing life in terms of self (SN 12.15; SN 12.17). Instead, life is viewed as merely natural phenomena; and suffering is viewed as being caused by ignorance (rather than by selves or persons).