The broader implications may take her some to process. There was an ancient, lost civilization with much better technology (and possibly worse magic?) which destroyed itself completely, leading to a long dark age and the rise of religion. This might help recontextualize some previous information! (Also, Sinnah is many centuries old? Are kitsune immortal, or perhaps simply serially reincarnated? This might be insensitive to ask and she shelves it for later.)
There are radio transmissions, but the general public seems to be unaware of them; the information clerk mentioned rumors about ancient artifacts but Tanya didn't have the context to understand that yet. She was worried about making enemies by disrupting an existing monopoly, and mystified by them not making more use of their monopoly. If someone found a working radio from two thousand years ago, surely they'd have reverse engineered it by now... but that only applies to simple, analog radio. If someone found a digital radio set from Tanya's first world, and had no concept of electronics, there might be nothing they could do but replace the batteries!
In that case, she has an obvious in: she can approach the existing owners of radio sets, whose dearest wish is probably to be able to make more of them and who have already thought of the most profitable uses and market approaches, and offer her knowledge. As an outworlder she'd be credible enough to merit a hearing, and she can also demonstrate receiving their transmissions with her orb. Since there are strong patent laws locally, she can apply for a patent that the the radio operators (who are based in this city) will want to buy. She doesn't even need to bargain for that much; even a one percent share in the profits of something as civilization-changing as radio would be more than enough for anything a private person could want.
She'll consult with Sinnah about this idea at the end of their session; she doesn't want to interrupt her obvious enthusiasm for studying magic. And then Tanya will have some follow-up questions for the information clerk.