Hope this isn't too broad. I tried to make it as easy to understand as possible. A list of these technologies would be great
Fusion power, practical
As the definition is by energy use and the required increase is several orders of magnitude this will require an energy source that is relatively convenient and for practical purposes unlimited. The closest candidate is fusion which has been fifty years from adoption for decades. From what I understand the technology is mostly already there, but the engineering problems involved are large and expensive.
If you prefer something more exotic such as solar power satellites orbiting the Sun or zero-point energy that is fine.
One of improved biotech or practical AI
You need to have some use for all that energy. That means either population well beyond the ability of natural ecosystems to support or a machine civilization. Since the machine civilization would have no real need for the planet (or indeed large growth or density) either, the first option is much more likely.
Basically, you need the ability to recycle the nutrients in waste back to edible food without going through the natural ecosystem in a sustained fashion. We probably have all the necessary technology for this already, but we do not actually know how to do it in practice, since nobody ever needed to. Space colonies might be the first place where this actually happens and we do not have those.
Space mining, affordable
Building such civilization would require huge resources. The resources would also be accessible at a reasonable cost. While Earth might have enough resources once we can tap resources of the sea floor and improve our mining technologies, making those resources affordable will probably require being able to access resources off-the-planet at a reasonable cost. In short the cost of space flight has to come way down. There are already people working on that and it probably does not require new exotic technology either.
Advanced medical technology or simply time
The real issue here is that for us to reach the necessary population naturally will take lots more time than developing the technology will. With natural growth I have seen estimates of few centuries, but those generally just extrapolate the growth in energy capacity not accounting for the actual growth in demand. We might never reach the population levels that would use that much energy naturally.
So you'd probably want something that forces the population to grow. Simplest solution is to drop mortality drastically and make humans not die of natural causes at all. Rejuvenation (to stop aging) and regeneration (to fix damage from injuries and disease) in short.
Both are being researched, but unlike the previous technologies we do not have the science for them at the moment. This means that predicting when we might have them or if we will even have them is difficult.
Even more difficult to predict are the social changes or the effect of other technologies resulting from this kind of medical science. The people probably could engineer their children for upgraded specs, for example.
The amount of insolation is orders of magnitude more than what we use currently. So even if we assume everyone on the planet will consume 10X more than Americans, we're still nowhere near that amount.
It should be obvious that Level I is silly since it depends on the star, and the size and distance the planet is from it; none of which have anything to do with technological level.
Since most used energy ultimately winds up as heat, the only way we could use the equivalent to the total insolation is by having an enormous number of space habitats. Fusion power would be high on the list for that.
Personally, I don't see us ever using or even needing that much energy, but I've no better insight into the distant future than anyone else. Realistically, I don't see much reason anyone would want to live in space. Perhaps when the A.I. overlords take over, and our civilization evolves into a solid state/machine one, then it may make more sense.