Final comments on using an Echo Studio with a Fire TV and/other devices for sound system purposes. In a nutshell, expect frustration, hope for the best...
Alexa Home Theater Mode Connection:
I turned off Wi-Fi on my Echo Studio, which was on even when connected via ethernet. I registered my Echo Studio, Fire TV Cube, Fire Recast DVR, and Apple TV 4K into static IP addresses. I was hoping this would stop the dropped video and audio signals from the Fire TV Cube when using it paired with the Echo Studio in Home Theater mode (which is a Wi-Fi connection. The Fire TV Cube and Recast are connected by ethernet, but the Echo Studio doesn't have an ethernet port so it is using Wi-Fi 5G.
Things worked really well the first day. Day two I opened the Amazon Music app on the Cube and nasty, ugly, horrible things occurred, including popping noises, dropped sound, glitchy video, and general mayhem. Several restarts later, and I gave up on the Music app. Unfortunately, the Home Theater mode between Cube and Studio no longer was stable, and for the rest of the day nothing seemed to completely fix it. But it did improve over time. Then just when I thought it might be stable, I paused a video to go fix supper. While gone the Cube went into screensaver mode, the screen went totally black, and the whole thing was just a total pile of garbage at that point. Several restarts later, and I gave up. I unpaired the Echo Studio and the Cube from their Home Theater mode and gave up on that. I wonder if the issue could be with the Cube as it is still a bit glitchy even after being unpaired. It was fine prior to any pairing of the two, but not the same since. I also wonder if having a Fire Recast in the mix is problematic, but I’m not going to pursue a solution on the Home Theater mode issues.
Bluetooth Connection:
Bluetooth connections between the Echo Studio and my Fire TV Cube, Sony Bravia TV, and Apple TV 4K work without issues. This method gives you the ability to use the remotes to control the volume of the Studio. However, this is the lowest audio capability which at best can only yield 2.1 stereo on a speaker system capable of producing same.
Optical Toslink Connection
I tested the Echo Studio with a toslink to mini-toslink optical connection between it and my Sony Bravia TV. This works fine, produces better sound in general, but it is more difficult to get set up and requires a bit of fiddling about with the TV's audio output settings options.
- Auto 1 option which outputs "only compressed audio without change" [whatever that means] works on Sony Bravia TV and Cube, but doesn't work with the Apple TV 4K. This option sounds better than PCM compression but the same as Auto 2 option. This option can pass Dolby Digital Plus.
- Auto 2 option which outputs "only compressed audio for multi-channel content without change" [whatever that means] works on all devices. This option sounds better than PCM compression but the same as Auto 1 option. This option can pass Dolby Digital Plus. Unfortunately though, it won't work with the Cube for some 4K streaming, for example, episodes of "The Grand Tour."
- PCM output works on all devices. This option has less sound quality as Auto 1 and Auto 2 options, and it cannot pass Dolby Digital Plus.
ETA on 30 Nov 2021: If the Echo Studio is connected via a toslink optical cable and no other connection than that, remotes from other devices can’t control the volume. For example, if you connect the Studio to your TV via toslink cable then the TV remote won’t control the volume of the Studio. If you have an Apple TV or other device connected to the TV, their remotes won’t control the volume of the Studio either. Even the Fire TV remote cannot control the volume in this scenario. According to Amazon, the Studio can be paired with an Echo remote, but not a Fire TV remote. (I didn’t even know they made remotes for Echos.)
If the Studio is connected to the Fire TV via the Alexa Wi-Fi Home Theater mode, then the Fire TV remote will control the volume of the Studio when you are streaming through the Fire TV.
If the Studio is connected to the Fire TV via the Alexa Wi-Fi Home Theater mode AND it is also connected to your TV via toslink cable, then the Fire TV remote will control the volume of the Studio when you are streaming through the TV or another streaming device such as the Apple TV. However, the Fire TV remote might not seem to control the volume at first, but if you press the volume Up/Down button on the remote multiple times, then it will control the volume. Kluge and nonintuitive for sure, but it works. But this means you will need to keep the Fire TV remote handy even when streaming through the TV, or any other non-Fire TV device that is connected to your TV.
Summation:
Echo Studio had terrific sound for a small HiFi speaker system. It is great for listening to music and other things for which you would likely use other Echo devices. I will call this "standalone mode". I assume it will be even better when paired with a second Studio and/or the Echo Sub.
As far as using the Studio as a home theater system via the Alexa Home Theater mode, it has been very problematic, glitchy on the Fire TV Cube, and quite honestly frustrating. YMMV of course.
Connecting the Studio directly to various devices via BT is quite stable, easy to control volume, but it yields the least quality of audio output, although it was still better than my older Sony HT-XT1 theater sound system which has 2.1 stereo at 270 watts with two downward firing 4" subwoofers and two forward firing midrange speakers. This is probably the best option if the Home Theater mode doesn't work. It is stable, easy to maintain, is reliable, and it just plain works.
Connecting the Studio via toslink optical yields pretty good audio, but it takes a lot of fiddling about in settings, and it requires the Fire TV remote to change the volume.
If you have just a TV and want something better than tiny TV speakers for audio output, then a single Studio connected either via BT or toslink optical cable are good options. You can pair it with another Studio, but then you are doubling the cost and approaching what a decent 5.1 stereo soundbar will cost. If you want a higher end theater sound system you are better off spending hundreds of dollars more and getting a good 5.1 or 7.1 stereo surround system.