HDMI ports are not 2-way, they’re either IN or OUT. But some HDMI port that is an input port may have an audio return channel (ARC) feature that returns the audio portion of the signal back to an audio device like a receiver for processing.
The HDMI ports on a TV are probably mostly just input ports, but you can check to see if yours may have an HDMI out or not. It just depends on how they’re configured. So I guess I might have mis-spoke when I suggested earlier that an option might be to use an HDMI out from your TV to drive that HDMI switched device that has a Toslink out.
The HDMI from your Roku (or in my case, my NVidia Shield TV, or in other cases, a BlueRay DVD player for example) is an output port. Now if the content you watch on your TV is exclusively from your Roku, then you can drive the HDMI out from the Roku into an HDMI in of switcher I mentioned, then use that device’s Toslink or audio out to drive the TV Adapter, and feed that device’s HDMI out to your TV. But if you also watch other non-Roku content from your TV, like over-the-air TV channels or other contents from wifi that your smart TV supports, or other device(s) that may come in to your TV like a DVD player or something, then the approach above would not work.
That DAC with Dolby/DTS decoding that you mentioned you just found would be perfect for your Oticon TV Adapter, though. Then whatever you watch from your TV, either the Roku or the OTA TV channels or other smart TV contents from your TV, will be heard through the TV Toslink.
The only concern I may have is whether that DAC’s volume level is remembered or not if you power cycle it each time. If not, then you may have to keep it powered on 24/7 so you will always get the right preset volume level that you like going into the Oticon TV Adapter. It may not be a big deal because it’s really not a high drain device anyway.
One little quirk about the Oticon TV Adapter that I ought to mention to you, though, is that if the analog audio level coming into it is low enough (below a predetermined threshold), it may still work fine, but after so many minutes, it will go into stand-by because it assumes that there’s no audio activity at the input. So you will need to set it at a volume level high enough to keep it detecting above-threshold audio to keep operating. But since your already have your Genie 2 program turned down to -9 dB, you should be able to set the audio in to the TV Adapter hot enough to keep it from going into stand-by.