Propaganda as defined by the Encyclopaedia Britannica is the "dissemination of information—facts, arguments, rumours, half-truths, or lies—to influence public opinion." While organizations commonly characterized as "Big Green" or "Big Oil" may both have used propaganda-like strategies, that doesn't take away from the fact that an organized Twitter disinformation network definitely falls under this definition, whether "Big Oil" runs it or not.
You exactly described Big Green and Big Oil propaganda - to influence public opinion. Your definition explicitly mentions "facts" so therefore Big Green fits too.
The bias you try to point out is not present within me. I also have no proof that big oil is behind this. It's only a guess.
I also agree with your thinking. I'm guessing green energy companies are likely running digital propaganda campaigns trying to sway people away from oil.