It’s a good question but impossible to answer, for 2 main reasons.

Firstly, ‘average Christian’ is very difficult to construct. Just as today, there was in the 4th and 5th centuries a range of Christians, and the answer is very likely going to vary by geography, language, ‘level of devotion’, etc.. To the point at which constructing a mean or median believer is going to be arbitrary to the point of useless.

Secondly, very little evidence survives to point us to what ‘ordinary’ believers knew and believed, because they were not figures of interest and so their writings or other evidence were not preserved.

However, we can make some forays into the question:

Firstly, the answer must depend upon geography. In the Latin West, very likely not-very-much, because the 4th and 5th century debates were primarily Eastern and Greek affairs to which Latin bishops were a party, but not a well-informed or fully-engaged one. One can reasonably conjecture then that ordinary believers in the West were perhaps aware there were various councils going on, those that the western bishops attended or engaged with, but not necessarily the specifics of doctrinal debate. Those in Rome were probably better informed, particularly in terms of the political alignment between Rome and Alexandria.

Those in Antioch would be keenly aware, because there was an ongoing schism in the church there into 2, and for a time 3, different communities. Having a very localised instantation of theological division would no doubt heighten awareness. One form of evidence that is suggestive are homilies, precisely because they are directed towards congregations. Chrysostom’s sermons, for instance, show that he touches upon and deals with doctrinal matters related to contemporary theological disputes, without being super-technical. It supports my hypothesis that ordinary believers would be aware, if not greatly informed.

There’s a famous passage from Gregory of Nyssa:

Everywhere, in the public squares, at crossroads, on the streets and lanes, people would stop you and discourse at random about the Trinity. If you asked something of a moneychanger, he would begin discussing the question of the Begotten and the Unbegotten. If you questioned a baker about the price of bread, he would answer that the Father is greater and the Son is subordinate to Him. If you went to take a bath, the Anomoean bath attendant would tell you that in his opinion the Son simply comes from nothing.

from De Deitate Filii et Spiritus Sancti, which suggests that in Constantinople literally everyone had an opinion. I suspect that this too is at least somewhat exaggerated. Nonetheless, it gives the suggestion that believers were aware, and had opinions, on this significant theological disputes.

So, in short – we’re not sure but it’s not unreasonable that non-clergy were aware of these debates and had opinions on them.