Scifi generalises most advanced races with bio-tech. I wouldn't rule out the possibility but a change is needed than the usual sins ships. On top of that as with most advanced races its highly considered mastering bio-engineering is the ultimate peak in technology terms before transcending to pure energy:

I'm going to do this point-by-point, to keep it as easy-to-follow as possible.
1. Bio-tech =! bio-ships. I do not object to the idea that a bio-technological device, consisting primarily/predominantly or perhaps entirely of biological components would not be a fantastically advanced piece of technology, or the idea that a hyper-advanced civilization (there's a difference between that and a 'race', I'll get to that in a moment) could build a bio-tech system that equals the purely synthetic systems of a far less advanced civilization.
However, said hyper-civilization would be far better of building synthetic devices that, with their hyper-advanced state, would be, quite simply, godlike compared to the tools of a technologically-inferior power. It is, simply put, a monumentally stupid idea to use a state of hyper-advancement to build a biological tool that works just as well as the same example of the neighboring empire that happens to be a million years younger.
Unless your state of hyper-advancement is so great that you pretty much do things for shits and giggles anyways.
2. Bio-ships =! the end-all-be-all of spacecraft. Bio-ships, are, quite frankly, an extremely naive (at best!), if not extraordinarily stupid idea IRL. In fiction, the concept can be executed quite well; witness Peter F. Hamilton's Night's Dawn Trilogy, a major part of which is biologically-based spacecraft and orbital habitats. But in this place we call 'reality', or 'real life', a bio-ship will be far more vulnerable than a conventional ship of metal.
Think about this; the first pieces of armor were composed of leather and wood, during the early Ancient world, such as the time period that the Trojan War would have taken place during, as well as the Greco-Persian conflict (and the historic Battle of Thermopylae), and the Peloponnesian Wars. By Roman times, shields were often made of metals, for increased strength, and breastplates were as well.
Fast-forward to medieval times, and you have plate armor composed of iron and steel to protect knights. Put a knight in steel plate-armor up against a Spartan with leather armor and a wooden shield (remember, that's organic/biological technology!). What happens? Fairly obviously, the knight will win- if only because the Spartan is simply unable to do any damage to the knight, thanks to the steel plate.
In the same way, a biological spaceship would be pathetically vulnerable to concentrated radiation- which is both abundant in space already, and easily produced by items such as nuclear and antimatter warheads- and any civilization which can build interstellar spaceships can also build nuclear weapons, at the very least.
3. Bio-engineering is not the ultimate peak of technology. Humanity is working on bio-engineering concepts now. Part of the reason is that the term is intrinsically broad and general. The other part is because we're always figuring out new ways to integrate technology with ourselves and into our lives.
Quite frankly, considering that it has been mathematically proven that mathematics will never be finished (IE, it will always be a growing field, with new formulae and equations being derived or formed all the time), it's quite possible that science would similarly be forever open-ended and unfinished.
That being said, the ultimate peak of technology would be, IMO, the ability to form a post-scarcity, post-human, post-singularity, society. And no one knows what that would look like, since by definition any society formed based on the singularity is unpredictable (that's why it's called 'the singularity'; it's a metaphorical event horizon beyond which we cannot predict what things would be like).
4. It is impossible for a species or civilization to transcend to pure energy- unless you mean that they do a mass mind-uploading into a gargantuan series of computer matrices. In which case you should really say "transcend into pure information". Energy-beings are a brainbug and a trope of fiction- they simply cannot exist.
5. Civilization =! 'race'/species. Look at humanity now- the entire species has wildly varying technical capability and access, whilst general "Eastern/Western/3rd-World" civilization tends to be grouped into general capability- for example, the majority of Western civilization has cheap, rapid mass-media, medical, and transportation access. Compared to 99% of 3rd-World countries, who lack all of those.
It gets even greater- the United States, Russia, and China, all of which either are, were, or are probably about to be, superpowers, have the ability to put men in orbit- and even on the Moon, if we're willing to spend the money. Nearly the entirety of the rest of the planet's nations are unable to even attempt to do so.
I don't argue about the fact nano-tech is superior to conventional technology. My favourite race will remain to be the Vasari but one thing puzzles me as to how they could loose at all. Must be something we havent already seen-- bio ships or some freak of nature terrorizing there space. My perceptions ofcourse could be influenced by what i've come to know of many scifi races with the same preferences and also the fact i encounter races like the zerg in starcraft 2.
6. Nano-tech is NOT superior to conventional technology. Yes, there are some applications that it's far more suited to, but on the whole, a nanotechnological device is likely to be outperformed, for both cost and speed, by a conventional system. Nanotech manufacturing will never replace conventional manufacturing and assembly techniques, unless it's a fairly specialized item, like a quantum-level computer. Nanotech weapons are pretty much useless compared to a plain old-fashioned nuclear weapon, or even just lumps of metal chucked really really fast.
That Vasari nanotech is so superior and advanced is more because of Rule-of-Cool than anything that's plausible or scientific.
7. First off, the correct term is 'lose' it all. One 'O', not two. Secondly, it's quite simple- the Vasari may be the most civilization we know of in SINES lore, but, since the game is generally all we have to go by, the other factions are capable of holding their own against the Vasari warships and battlefleets.
Vasari technical par excellence relates more to their construction, maintenance, and movement capabilities, as well as certain more esoteric weaponry such as phase missiles (bypassing shields is quite the accomplishment) and the Kostura cannon (shooting Phase Nodes? YES).
It's entirely possible that the Vasari simply came across a power that their own technological superiority paled in comparison to- one of the resident theories of the forum is that the Vasari's nemesis is the civilization that constructed the Phase Jump Inhibitors- remember, the Vasari found them, and discovered that their ridiculously overpowered nanotech could replicate the PJIs.
It's also possible that the entire Vasari nemesis is a big elaborate hoax, or is hive-mind-nanobot-mind-controlled-Vasari hunting the not-hive-mind-nanobot-mind-controlled Vasari.
8. The Zerg of Starcraft and SC2 are nothing special. Look up the Tyranids. Just type "Tyranids" in Google. It's that easy. And you'll find just what Blizzard more-or-less copied the Zerg off of (the Tyranids have existed in some form since 3rd Edition Warhamer 40,000, so circa 1989-1991).