I cannot answer your question, but I can provide you with one primary source—Orosius. Orosius (born c. 375, died after 418), is one of our most important sources for the subject. He describes the loss of the library in a relatively mournful manner. However, do you think your question might be assuming a relatively modern perspective on history and knowledge?

Here's his description: The flames spread to part of the city and there burned four hundred thousand books stored in a building which happened to be nearby. So perished that marvelous monument of the literary activity of our ancestors, who had gathered together so many great works of brilliant geniuses. (Orosius, History against the Pagans, Book 6)

Coming a bit after Orosius, Richard de Bury wrote in his Philobiblon circa 1345:

Yet we must tearfully recount the dreadful ruin which was caused in Egypt by the auxiliaries in the Alexandrian war, when seven hundred thousand volumes were consumed by fire. These volumes had been collected by the royal Ptolemies through long periods of time, as Aulus Gellius relates. What an Atlantean progeny must be supposed to have then perished: including the motions of the spheres, all the conjunctions of the planets, the nature of the galaxy, and the prognostic generations of comets, and all that exists in the heavens or in the ether! Who would not shudder at such a hapless holocaust, where ink is offered up instead of blood, where the glowing ashes of crackling parchment were encarnadined with blood, where the devouring flames consumed so many thousands of innocents in whose mouth was no guile, where the unsparing fire turned into stinking ashes so many shrines of eternal truth!

etc.,

Slightly rambling, not the usual top-level, but I think there's a more complicated historiography question to be asked...

There was a great deal of knowledge lost with the burning of the library of Alexandria. This is a fact. They destroyed a great number of books for which there probably were no other copies, works from a vast number of cultures, places, and times. Early philosophy, art, culture, history, religion...

But that's not what people mean when they say "muh lost knowledge" is it? Because they're referring to some notion that the civilization concurrent with the library was more advanced than that after the library. If we were to measure a civilization, we would do so by its 'greats,' the most influential and celebrated works (which by and large won't disappear with one library or even one city) or by it's standard of living, like technology and health (something which was everyday, something ordinary people would have had constant access to, something that would survive the civilization itself, most likely).

So there's two versions of this question embedded in yours, the first having to do with lost technologies, as in, things they had that we still don't. There's also the speculative question, being, if they had access to those books, what might have they accomplished earlier than we did?

And as we know, the first question is resolved, and the second question is theory and speculation and not history (and if one wanted to speculate, the safest bet is 'not much,' since many discoveries were about access to tools and materials and not access to books).

But the first question is more interesting, really, because I think it's more to the heart of what you mean. Technologies (with rare exception) don't up and go. And of those, the examples we have are underwhelming, mostly because the trope often brings up Indiana-Jones-style lost superweapons and splendid utopian alternate histories. There's Greek fire for which we have many suitable alternates, in the ancient East they were making good-quality steel and now we make better, the Baghdad batteries which aren't all that complicated, the Antikythera mechanism which is cool but as mundane as it gets...

So, as a supplemental question, I'd ask; who originated the trope of 'disappeared super technology'?

Which represented a greater loss of knowledge: the burning of the Library of Alexandria or the sacking of Baghdad by the Mongols? I understand that in the latter case that some of the most valuable works were removed before the city fell, so perhaps it was not as disastrous as people commonly think?

I think people have blown this hugely out of proportion, and people have ignored specifically what Sagan has said. In the Cosmos Library of Alexandria scene he mentions a Greek astronomer, Aristarchus of Samos. He says that Aristarchus of Samsos apparently argued that "the Earth was one of the planets, that like the other planets it orbits the Sun, and that the stars are enormously far away. All absolutely correct. But we had to wait nearly 2,000 years for these facts to be rediscovered."

I really don't see what's so appalling about this statement and why everyone is so annoyed by it. The Library of Alexandria was destroyed, ergo this information (and much else) likely would've taken a long time to be rediscovered. Why is that so implausible? This hasn't been explained at all. It's just a massive circlejerk.