As a graduate student, I don't have the authority to suggest how the department should conduct itself
That’s incorrect. You absolutely have the authority to suggest improvements to the program curriculum, and in all but the most incompetently run of departments, your suggestions would be welcomed, and given at least fleeting consideration; in a really well-run department they may in fact be considered quite seriously. Whether they would be adopted or not in a separate question, but if they are not adopted, it’s not because anyone thinks you don’t have the authority to suggest them. Regardless, no one would think you’re overstepping your role as a graduate student by making a suggestion (as opposed to making a demand or coming across as someone who thinks they’re entitled to run the place).
I wanted to bring up the idea to the Department Chair that introducing some applications like JupyterLab, GitHub, and R to our future graduate students could be a great move to not only support the move to online learning, but allow students in our department to get additional skills that are widely used in industry and currently not offered by our courses, but for which I know a number of our professors use routinely.
It sounds like these professors you mention already see the value in what you want to propose. Why not try to enlist them as allies and supporters of your idea, while offering to do the grunt work of promoting it? For example, you could send them an email where you outline your proposal, say you are contacting them because of their interest in these software applications and that you intend to present it to the department administration (not necessarily the chair - see below), and ask whether they are willing to be included in the correspondence and to be mentioned as possible endorsers of the idea. Stress the fact that they wouldn’t need to get involved in the effort in any more substantial way than that if they didn’t want/have time to.
I have a good personal relationship with the department chair as well, but I still want to be cautious of how I approach this.
That’s good, and the department chair may be a good place to start. But it’s worth keeping in mind that the department chair is usually an extremely busy person who is stretched thin between managing a whole bunch of completely different aspects of the department. In particular, at all departments I’m familiar with (including the one I was chair of for several years), the chair would not get directly involved in detailed thinking about the graduate program curriculum - that’s simply too “micro” for the level of detail the chair is able to handle. Usually there will be other people below the chair — a graduate vice chair (sometimes called the graduate program chair or graduate chair), graduate program committee etc — who make those sorts of decisions (maybe with the department chair ultimately being asked to sign off on any major decisions).
I suggest that before you officially propose the idea, do a bit of l asking around informally to find out who are the person or people who are in charge of thinking about these sorts of issues within the department. This way you won’t waste people’s time and your own time getting bounced around from one person/committee to another, with the attendant risk of the communication being misdirected or misinterpreted at each step along the way.