It is not linear that plastic bags are worse for the environment than cloth bags or paper bags.
A kind of war has been fought over plastic. The EU has legislated the end of the so-called 'single-use plastic,' supermarkets and other companies are eliminating it from their offer, and there is no collective awareness of the adoption of paper or cloth alternatives that may be reusable. Yes, 'one-time plastic' is bad, but not for the plastic itself - it's precisely for the 'one-time-use' part. The following rule of thumb is as follows: useless things but use these things more often, and buy less new things. ( https://www.bbbags.net/ )
Are plastic bags worse than paper or cloth bags now? The answer is not as immediate as it sounds. It depends on the variables we look at. The plastic bags you are likely to find in supermarkets (or would find) are technically called LDPE - that is, "Low-Density Polyethylene". These thinner, low-polythene bags, as their name implies, are not biodegradable and can end up in the oceans, which is bad for the environment; however, ignoring the garbage factor and looking only at how they are produced, it can be said that they are a more environmentally friendly option than paper or cloth bags.
Because the impact of the production of these LDPE bags on climate change is low, taking into account ozone release, water use, air pollution, etc. According to a 2018 study promoted by the Government of Denmark for product life cycle assessment, an organic cotton bag has to be reused 20,000 times to have an environmental impact equal to an LDPE bag (analyzing all the associated environmental impact the production of both bags); already a conventional cotton bag has to be reused 7,100 times - the study is based on the assumption that organic cotton has a 30% lower yield rate than conventional cotton and is therefore supposed to require 30% more resources, such as water, to grow by the same amount. Even by adjusting organic cotton production to use less fertilizer and pesticides, conventional cotton stands out. The Danish report also assumes that cotton cannot be recycled as there is little infrastructure for textile recycling.
More information about LDPE bags: https://www.bag-wall.com/