Another read on this is that it is a legalistic debate between the Johannine community and the hellenistic “Jews.” John's community was dealing with being exiled from the synagogue. The word ἀποσυνάγωγος appears only in John, and three times. It means "ejected from the synagogue." Here and dealing with the healing of the blind man, there are many points where there is a sense that this group was in conflict with the reigning jewish community and was in exile from their previous social home.
But on "My father is still working," Note the following
The Septuagint Genesis 2:2, “ And God finished on the sixth day his works which he made, and he ceased on the seventh day from all his works which he made.”
-this is true in the syriac and samaritan bibles also
In the Hebrew, we have (NRSV), Genesis 2:2, “And on the seventh day God finished the work that he had done, and he rested on the seventh day from all the work that he had done.”
So here, it can be interpreted that God finished his work on the SEVENTH day (was still working on the seventh day) where the hellenistic greek jews who would read the septuagint would not have this confusion.
Just before in chapter four with the woman at the well, there is conversation about the differences between the samaritan torah and the judean torah. John 4:20, "Our ancestors worshiped on this mountain, but y'all say that the place where people must worship is in Jerusalem.”" This is a detailed discussion of the difference between the samaritan torah and the judean torah. The Samaritans worshiped at Mt. Gerizim while the Judeans worshipped at Jerusalem. This is one major difference in their texts.
For John, Jesus is, amongst other things, the Hebrew Torah made flesh (the word). Jesus' claim here, especially coming on the heels of the samaritan difference in chapter four, and his refusal to use septuagint translations in his scripture quotes broadly (as opposed to Matthew, for example, who quotes directly from septuagint). This may have been a legalistic difference between John's community and the broader hellenistic greek judaism. This may have been hammered home because John disliked the way that the text had been "degraded" when translated into greek. Ironically, we read this from a gospel written in greek.