You’ve lived over centuries?? Man — You gotta tell me what you’ve been eating…
Seriously - I try not to concern myself too much with matters that occurred in the Church centuries ago. Different times, different ideas, different cultures - just a lot different…
As I said in my closing, Just living Love - today and tomorrow is quite enough…I’ll leave the rest to the apologists…
The answer to your questions is an single - YES.
The Church is both. The Structure that we have today is a necessary result of the desire of the earliest Christians to uphold that Which Christ founded and prayed for.
Consider:
Most any group of any size will develop some sort of structure for the purpose of coordination, governance, handling of monies etc as well as providing a forum for handling rules, disagreements, and other matters necessary for the good of the group as a whole.
So - should it be a surprise that the Christians began developing organizational structures early on?
Christ founded a Church - a community. That community is comprised of people who have committed themselves to “live as Jesus wants us to” ( or at least we try:shrug

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Jesus also prayed that His community be One as He and the Father are one…(John 13:34-35) A veerryy close relationship…
Jesus then gave the Church Authority to Bind and Loose - “Whatever” (Mt 16:17-19 and Mt 18:15-18)…Pretty broad authority wouldn’t you say?
Jesus then told us to take obstinate and contentious issues and “Tell it to The Church”
AND that we are to “Listen to the Church” lest we be treated as a heathen and a tax collector (Mt 18:15-18).
Then - when the early Church faced it’s first doctrinal crisis - the Early Christians demonstrated what would become the trademark method for dealing with such issues. They held a council, came to a decision and promulgated that decision in writing (Acts 15).
As the Church grew bigger and bigger - it became more and more necessary to have better communications, to have a way to review writings, to debate issues and most especially to gather, collate, copy distribute and teach only the Truth of the Gospels.
So - over time - the institutional structures that we have today developed, not as something imposed from outside and separate from the faithful as individuals, but rather as an outgrowth of the desire on the part of the group to “live as Jesus wants us to live”.
They are an outgrowth of the desire to “be one” as Jesus and the Father are one.
They are the result of the needs and desires to protect, defend, copy, distribute and teach the truth of the Gospel.
Not sure I explained that well…I hope it helps you understand some.
Peace
James