Complexity or density of communication has to both with the modalities involved (auditory, visual, etc.) as well as the richness of what is conveyed (how much information is conveyed in each modality). I spend the majority of my time focused on the modalities portion of communication because it is most relevant to the discussion around communicating via different methods such as text vs phone vs video. However, you are correct to point out that how rich the communication is depends on the modality.
The most common way this shows up is an issue of hardware - if the camera you are using is of low quality or the internet connection cannot support it, the video signal is often compressed and information is lost because of this. What is available in frame versus not in frame also affects the richness. If I’m sitting in a chair and the camera can only see the upper 3rd of my body, you would be unable to see what my legs or feet are doing, which affect the richness of the signal. In addition, as you’ve mentioned, people act different in different situations - they may not communicate the same body language in all modalities. Human behavior itself is important when it comes to the richness of information conveyed. In fact, people often modify their behavior in response to the reduced richness of the signal! People have ‘phone voices’ when they are on the phone where they exaggerate or flatten their voice to counter information that is lost via transmission depending on their pitch register and other factors. A ‘radio voice’ is another common way in which people modify their speech over an auditory medium to enhance the signals they care most about. When communicating purely via text, people can add images and emojis, or change the very message itself to be sure important pieces of information are not missed (such as adding lol or /s to convey meaning). Even over visual mediums people find ways to change their behavior in response to the modality and may exaggerate certain movements or learn to conduct themselves in specific ways to ensure the communicated message best matches their intent.
I think it’s also important to note, as you did, that these changes and differences aren’t always intended and are a direct response to the medium and how we think, as well. It’s not uncommon for people to be entirely uncertain where to look when using a camera to project themselves to others. People often get nervous and change how they interact when speaking in public. Observing a child who’s only just learning that you can talk to people over phones or video chat exposes all kinds of idiosyncrasies of communication. People go to school to learn how to act on a stage, in front of a camera, over the radio, and through other mediums to become better communicators in mediums where richness might be affected or where they want to learn skills to better convey the same message.