Sonic technology is just a different form of energy transfer.
- Modern day tools and weapons rely on the transferral of kinetic energy. Screwdrivers physically touch screws. Bullets impact the target based on their travel speed.
- Laser tools and weapons transfer energy using lightwaves.
- Sonic tools and weapons transfer energy using soundwaves.
These are all essentially the same: they transfer energy in order to manipulate something.
Think of it this way: a VW Golf, a Tesla Roadster and a hovercraft may require different technological levels in order to build the vehicles, but they will all get you from point A to point B. They are all vehicles, even though one is technologically more advanced than the other.
Does your question include e.g. a civilization with a more basic grasp on sonic technology, or are you only interested in those who use sonic technoloqy equivalent to the Time Lord sonic technology?
Anyone has access to any technology once they research it.
So, all in all, who has sonic tech? Is it the Time Lords? Is it everyone? Is it Time Lords and the Nursery Fleet?
Sonic technology is accessible to anyone who has developed it. It is not exclusive to any particular race; but there may be prerequisites for a civilization to advance to the needed technological level.
Your question is no different from:
Which civilizations wear glasses? Is it A? B? Everyone?
Every civilization is capable of making eyewear, as long as they've already invented glass (or any substitute that allows grinding it into a lens).
Imagine if a civilization invented LASIK before glasses (therefore never needing to develop glasses). Do they count, because they are technologically capable of making glasses, or do you discount them because they choose to not make glasses?
Which civilizations use agriculture? Is it A? B? Everyone?
Again, every civilization should be able to use agriculture. The question is whether or not they bothered to do so.
It is irrelevant for those who do not eat organic food (e.g. Cybermen), and it may be irrelevant to those who are able to consistently hunt for a living and have never run into any food scarcity issues.
Similarly, sonic technology is accessible to anyone who has mastered the preresuisite technologies and wanted to develop sonic technology. Since the Time Lords are stereotypically technologically ahead of most other civilizations, they are of course likely to have unlocked many advanced forms of technology.
Modern day humans are already capable of basic sonic technology.
As I said, the core of sonic technology, using soundwaves to transfer energy, is accessible to anyone.
Have you ever been at a concert with massive speakers, where you could feel your chest vibrate when it plays a heavy bass? That's the core of sonic technology: a soundwave that makes a distant object vibrate.
Speakers in and of themselves are obviously also a form of sonic technology. They create soundwaves that manipulate our eardrums.
The only difference between a concert speaker and the Doctor's sonic screwdriver is a matter of precision. Our current speaker broadcast sound in all directions, whereas the Doctor's sonic screwdriver is capable of a targeted strike (e.g. manipulating a specific component in a specific device).
A direct answer to your question.
It depends on how you look at it. Since every civilization may be able to develop sonic technology independently, we can't really be sure how many civilizations are using sonic technology without checking them one by one.