Are any commercial plastics made from plant matter currently. I expect it can be done in a lab but I am wondering about cost competitive tonnage quantities.
The original answer only gave a link to a commercial bioplastic producer. The answer has been edited to provide more information.
Yes there are. Here is an example: Biome Bioplastics
European Bioplastics (an industry group) estimates that the global production of bioplastics was about 2 million metric tonnes in 2017. They forecast that this will increase to almost 2.5 million metric tonnes by 2022.Source
One estimate puts the market value of bioplastics at around 6 billion USD in 2018 and growing to almost 15 billion USD by 2023. Source
Common sources of bioplastics are starches (like corn), cellulose and aliphatic esters.
Commonly, bioplastics are used to make compostable/biodegradable packaging and films, as well as disposable cups and utensils.
Biomass polymers can and must never become more than a niche product for guillible customers, or for specialities.
Any attempt at upscaling these to large tonnages (that can actually make a dent in our oil consumption!) inevitably leads to food shortages and/or depletion of soils and biodiversity.
Same is true for biofuels. Photosynthesis is far too inefficient (max. 3%, compared to 15% for PV, and much more for thermal solar power).
Food production is bad enough for the environment as is. Don't make matters worse.
Actual examples for bio-based plastics are of course cellulose derivates, packaging made of starch, then polyols for polyester or PU, and the notorious sugarcane-ethanol based polyethylene.