“He had several levels of clergy under his own authority. “
No he didn’t. He was an apostle, and strove with Peter over this and that, and they met as a group of elders to work things out, and they did so.
There are two ordained offices in the church: elders(or bishops if you prefer), and deacons.
No pope, head elder, or what have you.
It is interesting that you mention Paul as a super authority, since Peter according to RC doctrine is supposed to be the overall head, but I digress.
No he didn’t. He was an apostle, and strove with Peter over this and that, and they met as a group of elders to work things out, and they did so.
That is working things out with equals. The fact is that Timothy was under Paul, and the local deacons were under Timothy. The hierarchy was established very explicitly.