I got a new TV late last year and had to get an inexpensive DAC because I'd previously had a 15-20 year old plasma that had analogue outputs and I was using an analogue-only little amp and speaker setup for sound, whereas the new TV had digital audio output only. The DAC I got was this one:
https://www.amazon.com/gp/product/B005K2TXMO/
I got it because Amir did some basic testing on it compared to another similarly cheap DAC and this one tested out decently and much better than the other (
https://www.audiosciencereview.com/...view-and-measurements-of-budget-20-dacs.1316/).
I believe I did have to change the TV's audio output setting from Auto to PCM (on Auto, some sources would play sound and some wouldn't - obviously the ones that would were streaming in PCM while the ones that wouldn't were streaming in Dolby Digital). The DAC itself has been set-it-and-forget it - I stuffed it into the back of my TV credenza and haven't touched it or even seen it since I hooked it up. It works great. I had to supply an iPhone-style 5V USB wall plug, but the unit came with its own USB power cord
and crappy-looking but totally functional optical audio cable. So I can recommend it.
I can't guarantee it will solve your problem, though, because your current setup seems like it should work as-is.
One final note, which doesn't sound like it's relevant in your situation, but just in case: The optical audio output's functionality on TVs varies from brand to brand and sometimes even model to model, and is not always thoroughly or accurately documented in the user manual. Specifically. some TVs do
not reliably pass digital audio through the TV from connected digital source components. So for example some TVs will output audio over optical from the TV itself, but if you have a Blu-Ray player or streaming device connected to the TV via HDMI, the TV won't pass that audio from its HDMI input out to the optical output. All the TV's I've ever owned
have done that pass-through. But I have read reports online from owners of other TVs that some don't.