I've taken a public speaking class in the past, and it was certainly a good place to get more practice being up in front of a crowd of people to speak and be in the spotlight. Being a TA college was more beneficial on the soft skills front though as it forced me to really listen to my students, understand why they were confused about something, and maintain the patience needed to actually get them on the right track. In both cases, the real benefit was having a regular platform that forced me to be social and present for a group of people, and in the case of teaching, I had to learn to do all of that under the pressure of people holding me accountable (i.e. if I said something wrong or steered them wrong, they would either stop coming to my tutoring sessions or call me out for it). Having opportunities to regularly practice being outside your comfort zone and being held reasonably accountable for how well you perform seem to be key to getting anything out of such experiences. Classes that are just you reading about how to be a good public speaker or recording yourself in front of a webcam to send to a teacher for grading are what I've seen from some online courses, and I don't think you're really getting much out of them. Or, at least, I'd check out Coursera (https://www.coursera.org/learn/public-speaking) for free classes if you just want information.
In lieu of a paid class, it might be worth looking into possible volunteer opportunities where you are teaching something you know or having to be a leader of something (like a sports coach of some sort) that really drive you to put your soft skills to the test in the real world without having to sink money into it.