Since the new remote came out ⁓2^(1/2) months ago, many people posted/commented that the volume control & mute buttons are not showing up/disappearing after pairing with their device.
It's not an issue with the app or your phone. It's an issue with your TV.
Different manufacturers handle HDMI-CEC differently, and some manufacturers (notably Samsung) doesn't allow external devices to control the internal volume via software remote.
Read more about it here
My TCL 6 from 2018 is top tier except for the volume through the Google TV/Home apps. I can use the remote control to change the volume fine, but to change the volume from my phone I have to open the Roku app and then I can adjust it.
On my cheaper TCL 4 series downstairs, I have completability to control the volume using the Android TV software remote app.
While I assumed I knew the limitation reason, glad to have someone else bring it up and point it out.
Portion of the article you posted:
There are three notable issues I ran into when using the new remote over the last weekend. Sadly, the first one isn't really Google's fault. . . As you can easily see in many of my screenshots above, volume controls didn't work for me at all. But that's not Google's fault, it's mine and Samsung's. Though my TV has Anynet+ branded HDMI-CEC functionality and should ostensibly be able to accept the required volume commands from my Chromecast with Google TV via HDMI, my TV won't actually allow external devices to control the internal volume. Every manufacturer handles HDMI-CEC a little differently, and the version in my TV can apparently pass volume commands back through to an external device, but it won't work for my TV's built-in speakers. (Thanks, Samsung.) That means that although my Chromecast with Google TV can adjust my TV's volume using IR on the included hardware remote, it can't be configured to allow the software remote to adjust my TV's volume itself. .
If your TV has Android or Google TV built-in, Google tells me that this won't be an issue, and volume controls will work correctly without any finagling. Other HDMI-CEC implementations may also work for internal TV volume. So far as I can tell, even just a soundbar would likely fix the issue for me — and when I get around to that or rebuilding my receiver/speaker setup, I should be fine. There's also another workaround you can do on some Android TV devices, like the Chromecast with Google TV, telling them to control volume internally on their own (Settings -> Remotes & Accessories -> Set up remote buttons -> Chromecast volume), and that could be a solution for some — though it can introduce its own potential problems.
Oh, "the" software remote. Now your post makes sense to me.