I understand the issue, that you have to physically go and press a button on the streamer itself.
this remote has both IR and 2.4GHz modes.
not sure how this is in the vim3, but my streamer came with a IR remote, and I taught the T3 remote IR power button to do the same action as my streamer remote’s power button.
so if I want, I can use IR to turn on/off the streamer.
now this must be working for you (given you properly taught your T3 remote power button to do what the streamer’s remote power button does).
if not - you need to look at the bl301 thing, or seek help for your device.
regarding the power menu - when you’re on the 2.4GHz mode of the remote, you can configure any button to do anything you want, through the usual key mapping.
there are several threads describing how to change it, but as far as I know, when the streamer is in sleep mode, any button should wake it.
again if not - there’s an issue beyond the scope of the T3 remote, and you should start a new thread, or search your issue to solve it.
hope it helps you.