Roma Aeterna

There are three kinds of issues involved here. First of all, yes scientific and technological progress was made in OTL western Eurasia during the Middle Ages, although the bulk of it occurred in the latter half of the period, during the High and Late Middle Ages span in Europe and the Islamic Golden Age in the Middle East. On the other hand, western Eurasia did suffer greatly from Rome's collapse, the socio-economic regression and political fragmentation in manorialism and feudalism, and the break of Mediterranean unity caused by expansion of Islam. ITTL nothing of the sort exists, Rome keeps being basically prosperous, the integrated proto-market economy and urbanized society the Principate created across the Med lands remains strong and gets expanded to Central and Eastern Europe several centuries before OTL Christendom did it.

As a result, Rome evolves directly from early Principate conditions into High/Late Middle Ages and Islamic Golden Age ones without the baggage of feudalism centuries earlier than OTL, precisely because it misses the collapse and keeps building on its own achievements. It also helps the Roman, Chinese, and Indian sophisticated civilizations create an efficient proto-global trade network to exchange goods and ideas across Eurasia since Principate/Han times. So Rome evolves from Principate to Renaissance in one unbroken trend, about a half-millennium earlier than OTL. The TL tracks such progress all the way to mastery of Renaissance signature techs.

Since its society remains highly dymamic, as much as OTL Europe if not more so, it is only natural this progress pattern holds true all the way to industrialization and the Information/Space Age, so Rome achieves both pretty much with the same temporal advantage in comparison to OTL, industrialization by the half of the second millennium, 21st century technology by the last quarter of the same, at the very least. One might even argue that rate of progress may be slightly quicker yet, because of greater amounts of brainpower and resources, but I suppose OTL Europe pace anticipated by a half millennium might be a prudent aestimate. On the other hand, I see no plausible reason whatsoever why TTL Rome should be expected to be any less dynamic than OTL Europe. 

Moreover, I am also persuaded OTL modernity failed to realize its full potential of technological progress in certain fields such as space, energy, and biotechnologies, and since the factors that held back our world do not seem especially relevant here, the 21st century level equivalent for Rome is more advanced than OTL in those fields. The TL's final picture of modern Rome does represent this advantage, and it is assumed they achieved this level with the aforementioned half-millennium difference.

Last but not least, I'm left dubious if OTL 21st century did the very best an equivalent advanced civilization in other fields such as cybernetics, materials science, IT, nanotech, and so on, or if there was unrealized potential to do somewhat better. I lack sufficient knowledge in these fields to make the informed judgement I made for space, energy, and biotech. If potential to do better in the other fields did exist, modern Rome might well have realized it because of its resources advantages.

So there are three levels for this issue: first, successful Rome during its post-Classical history accumulates an advantage of at least about half a millennium in technological progress which holds true throughout its history; second, when it achieves 21st century equivalent several centuries earlier, it is even more advanced (by a few decades, probably) in certain specific fields where OTL failed to express its full potential; third, such an extra advantage may or may not be true across the board, but since the author is uncertain about this and lacks exhaustive knowledge, the TL assumes it does not occur.