There is one last resort even if you can’t find any information out about the remote. It’s expensive and a little weird, so you probably won’t want to use it. But just in case I’ll go ahead and mention it. (I myself am quadriparetic and can’t push buttons on a remote, so I’m always tracking other options.)
There is a South Korean company named Naran which makes a “robot finger” that is just a tiny actuator. The finger is called “push.” The push costs $49 by itself, but then it can only be worked from a phone that it was paired to with Bluetooth.
If you also get their $99 bridge, you can then access their IFTTT channel. So now you have a button pusher that you can attach to pretty much any existing device and operate by IFTTT. One bridge can support I think up to 40 of their micro bots.
So for $200, you could get two Push actuators and the Prota bridge and have integration with SmartThings or echo.
If you built a little stand to hold the two microbots in the right position over the remote you could still slide the remote out and use it by hand. But then you have to remember to always put it back in the stand so you can use it with echo the next time.
So like I said, weird, and expensive, but it should work. It’s the kind of thing that would be worth trying for someone in my physical situation, but probably wouldn’t make sense for someone who is ablebodied.
https://www.amazon.com/Starter-kit-MicroBot-Push-Sugru/dp/B01JRYT6L8/
So just something to keep in mind if this is a use case that you really want to solve and you can’t find out anything more about the remote and you don’t want to go with one of the maker solutions that require soldering things to either the remote or the TV lift. The microbot has the advantage of being prepackaged and not damaging the existing remote. 