The main goal of reducing single-use plastic is to deal with people just throwing it away on the street or in nature, resulting in animals trying to eat it and dying. When it comes to climate change, using plastic and simply incinerating the waste is probably the better option.
Taking oil out of the ground, making it into plastic using energy and chemicals and then after use dumping it into a landfill is bad for the environment.
Methane is produced when 'bio' waste breaks down in anearobic environment.
Composting is an aerobic process. So yeah, CO2 produced there. But significantly less harmful than what happens to the same stuff in a landfill.
Although in that case, methane may be captured. Of course never 100%. Perhaps far from it.