To add to this (because I’m a goddamn nerd) the first toothbrushes, made from boars hair for the bristles and either bamboo or bone handles, were invented in 1498.
While there’s no set time period analogous to our modern eras in Dragon Age, there are a few things we can look at to try to range it.
Gunpowder was discovered in 870 CE. Cannons were invented in 1347 CE, and the Qunari have access to cannons and bombs via Gaatlok, so we can assume that at the least the Qunari are existing in a post-1347 CE time period.
The Orlesians are modeled around pre-revolutionary France, the French Revolution happening in 1799 CE, so so far we have a setting set somewhere between the 14th and 18th centuries CE.
But the big tell of scientific advancement across all of the nations and kingdoms is Varric Tethras and the Randy Dowager.
Varric is an author, he writes books. Specifically, books for enjoyment and pleasure reading. To write books like that there is a base assumption of high literacy and more free time for both nobility (Cassandra) and commoners (Harding). Higher literacy also requires a higher availability of literature, and the time intensivity of writing, transcribing a book by hand meant that Varric’s book would not be widespread if we’re working in a world that still requires scribes and monks to hand write each page while following a master copy.
Enter the most important invention in human (and likely Thedosian) history: the Gutenberg Press.
The Gutenberg Press was invented in 1440 CE and was responsible for an ASTRONOMICAL leap in literacy and literature. Books became accessible, they became easier to make and multiple copies could be cranked out quickly. This meant that what could be created and written and published went from a select few (usually religious) texts to pretty much anything. Varric is an author, his books are widespread across Thedas, and in order to have the reach he has the printing press would have to have been around for at least a decade or two (1450-1460 CE). It takes a while for an invention like that to create jumps in civilization, so we’ll say a cool ~1460 CE for the publishing of his first novel.
The next part is the Randy Dowager. The Randy Dowager is a quarterly magazine published and distributed across Thedas every few months for consumption by the masses. It features news, gossip and speculation. It’s not a traditional magazine like we’d imagine in the modern sense and would be much closer to old periodical literary journals. The first of these ever was published in France in 1684 CE, and from there they gained quick popularity across the Western World. The Randy Dowager mirrors that, but is also one of the few in existence that we see referenced. For it to spread far and gain popularity, I’d give it around… say five years from first publishing and where it is in the first Dragon Age games.
Given all of that, the games take place in a technological and cultural amalgamation of between the Middle Ages and the end of the Renaissance, with technology and inventions that range between 1348 and 1690. Meaning that not only do they have ways to clean their mouths, your Love Interest does own a semi-modern bristle toothbrush and would have relatively similar dental hygiene standards to what we currently have in our own modern day.