What is the ruling regarding the Friday prayers of last week, and must they be re-offered as a full Dhuhr prayer, after it became clear that they were invalid due to the lack of settlement (istīṭān) and the incompleteness of the quorum?

Most scholars stipulate permanent residency (istiṭān) for the validity of Jumu'ah prayer, and that it is not valid if performed by temporary residents alone, nor with the number mentioned in the question. The majority do not consider it valid with this number. Even the Hanafis, who deem it valid with this number and by non-residents, stipulate that it must be performed in a miṣr (metropolitan city), which is any town where there is a judge to whom lawsuits can be brought. Based on this, your prayer was not valid according to the general opinion of scholars, and it is more prudent to repeat the Dhuhr prayer in full.