Before anything else: the state of the evidence for this question, especially in the first two centuries of the Principate, is not great. We have a lot of evidence from, say, Egypt, via papyri, and literally zero evidence for other places. It is an area where there is a lot of argument, and it is a system that was continually evolving through time, as you can gather from the lists you posted.

Altogether, in the first two centuries CE, there were between 150 and 200 officials to govern, in all capacities, the roughly 60 million souls under nominal Roman authority. That is an insane statistic, as many have noted (Hopkins 1980, e.g.). This ratio is often compared to other classic empires, like China. Of those roughly 200, half were holders of imperium by some means or another, and the other half were concerned with finances, a division which had not been clear-cut in the Republic.

Of those holding imperium, some were the regular ol' elected officials, theoretically under the control of the Roman people and elected by them: quaestors, praetors, consuls, propraetors, proconsuls. These men went to govern places which were under senatorial control, according to the divisions worked out in the early Principate. The others were appointed by the emperor to govern provinces which were Imperial by designation and by legislation, and these officials derived their authority via the Emperor himself. Some of the procurators in your lists fall into this category, while others were financial officials, which were theoretically separate. The finances of the Empire were further complicated by the division between "Rome's" money and "the Emperor's" money, which is very fraught in itself (see Millar 1977, Brunt 1990).

Of the non-financial bureaucracy, there were regularly sub-staff members, but a surprisingly small number: bodyguards, clerks, messengers, etc . These were typically of equestrian rank, though not always, and were generally called legati, a confusing word which in the Republic had applied vaguely to those receiving delegated authority from an elected magistrate, especially in the military sphere. To all these we add procurators, appointed by the Emperor, for a huge range of jobs. Some of them were the bosses of Imperial estates, others were involved in taxation, others seemingly in direct rule (like Pontius Pilate in Judaea, though he was actually a praefectus, technically).

The subjects of the provinces did not tend to care about the distinctions. In their dusty little village on the edge of the Sahara, the local army's centurions were a symbol of authority, and were frequently asked to arbitrate disputes, even though the centurions had zero actual authority from the Emperor or the Roman people. The same goes for Imperial procurators. The Emperor's chosen guy, who manages the vast Imperial estate which abuts on my tiny plot of land, is the local authority figure no matter what his technical status might be.

It is widely assumed (rightly, I think) that the administrative machinery of larger population centers played a major role in governance, especially in the more urbanized East. A good basic discussion of this, with references, is Ando 2006).

Ando, "The Administration of the Provinces," in Companion to the Roman Empire (Blackwell 2006).

Brunt, Roman Imperial Themes (Oxford, 1990)

Hopkins, "Taxes and Trade in the Roman Empire" (Journal of Roman Studies 70: 101-25).

Millar, The Emperor in the Roman World (1977).