It's an interesting and complicated question.
Mobius is a somewhat unusual plugin because how you control it doesn't fit well with the VST/AU notion of a "parameter". Most plugins have parameters that are bi-directional values, you can read them and write them, and hosts will show them using UI widgets like sliders and knobs. Mobius has those, but it also has a lot of "functions" which are one-shot commands rather than things that have a value you can see and change.
Neither VST or AU has a good way of dealing with those, what we can do is expose them as boolean on/off parameters, so you can start the function by setting the parameter to 1 and turn if off by setting it to 0. That makes it possible to control Mobius with host parameter automation but it's awkward and few people do that. It is far more common to just send it MIDI events as if it were a keyboard, but instead of playing a sound, those notes make functions happen.
But what you're asking for is really neither of those, what you have listed are what Mobius calls "modes", the state of recording, or the state of playing, etc. A mode is the way Mobius is behaving at a given time, but you can get into and out of modes as a side effect of lots of things. "Record Mode" therefore can't be a parameter that you turn on and off, It's a state Mobius can be in but it can happen as a response to many things. It's sort of like saying "I feel happy". There isn't a Happy Button you can press and release, you become happy as a result of other things. This may not seem obvious for something as simple as play vs. record, but there are reasons for that. One example, you can enter a state of recording after any of these functions: Record, Overdub, and Multiply. Sometimes you might want to know if you are specifically doing a Multiply, and other times in any state of recording, no matter how you got there so you can make something in the UI turn red.
We've experimented with a few ways of doing this bi-directional feedback for control surfaces. One option is a read-only VST parameter like RecordMode that you can test to see if it is recording for some reason, but you can't set it. Another is MIDI feedback through "event scripts" where you configure a script to run whenever the system enters a recording mode, and then that script can do anything, like send out a MIDI command to turn a light red.
Event scripts are the most powerful way to do this, but they're hard to set up right now, and don't do everything people have wanted.
Depending on how deeply you want to get into scripting, it's safe to say that right now Mobius doesn't have particularly good support for bi-directional communication with control surfaces or host applications that can behave like control surfaces. It will get better eventually, for GP the resurrection of OSC support that Mobius 2.x had may help as well.