When we burn wood in a very hot, low oxygen, environment, then the resulting charcoal is mostly the wood's carbon, and it is in a convenient form to sequester if stored so that the carbon doesn't have the opportunity to combine with oxygen.
Yes, it is more natural, and normally better for the environment, to allow the wood to rot, but that puts the carbon back in the air. Plastic, and nearly all non-metal stuff we use, is mostly carbon. The biosphere is good at getting at that carbon for structural and energy needs, so it will all degrade eventually. Biodegradeable stuff breaks down faster. When we get on top of climate change then that will be good. For the moment it is bad. Storing old plastic so that it doesn't combine with oxygen is sequestration. While we're getting on top of climate change, that is what we want.
Recycling doesn't automatically put more carbon in the air, since it might avoid the need to get more out of the ground. However the recycling processes are energy intensive because the old plastic is in a much less convenient form than new material. As with many activities, we need to evaluate recycling plans. For the next few decades it might well be better to store the waste, sequestering the carbon.
Another easy source of sequesterable carbon is agricultural, forestry and more general plant waste. Traditionally it has been burnt to get it out of the way. If instead we can treat it so that it breaks down more slowly then that will sequester carbon. Farmers might get some incentive income from this, to compensate for the space taken up.
While the pros and cons would need to be assessed, these ideas should be considered to try to reduce the impact of climate change while we await advanced energy options that will allow us to manage the climate.