Definitely not burning it, but pyrolysis has been suggested (basically "burn" it in an oxygen-free environment).
The plastics are heated to about 500 °C in the absence of oxygen. The longer molecules break into liquid fractions like naphtha and diesel, solid cuts like waxes, and lower-molecular-weight gases. In most plants, roughly 10% of the product is char, a by-product.
It's not without its drawbacks. Some gases are produced, and those are either burned to (partially?) power the pyrolysis process or are flared off. About 10% is reduced to char and would have to be disposed of conventionally (unsure of the environmental impact of that).
I don't have time right now to dive deep into the topic (just throwing off what I do know plus a link that explains it), but it's possible it's less harmful overall than just throwing it in a landfill forever. (Assuming the input energy for the reaction chamber comes from clean sources.)
Plus burning it allows those toxins to disperse across the environment while more traditional recycling can keep the toxins mostly concentrated on landfill/processing sites.
I think you could make an argument that even burning plastic in a firepit vs sending it to a landfill are roughly equal. Climate change and air pollution are both major issues, but so is plastic waste and microplastics working their way into everything. I have no idea of the overall harm of burning plastic is less than throwing it away; they both pollute the environment. I can see the the logic in thinking burning is a viable alternative.
Ideally, though, people would just stop using disposable plastic. Plastic is a fantastic material, but it was never supposed to be for "use once and discard" items. For creating durable objects with a decent lifetime, sure, use plastic. Don't use it as wrapping over another plastic object.
Incineration, is the standard way of getting rid of non recyclable waste (a lot of plastic can be recycled) not that green but it allows to produce electricity and hot water which saves some oil
I wish we could get a mobile plasma arc gasification truck that goes around turning rubbish into glass and hydrogen with no landfill, but until that day... Don't burn it, just do your reasonable best to avoid buying it.
Plasma arc gasification is very low emissions versus anything we currently do with it, but I would obviously prefer we just stop using plastic. Given how unlikely that is, the idea of plasma trucks going about eliminating the need for waste management infrastructure is at least fun enough to bring up conversationally.
Still not a great idea to burn recyclable resources. The stuff that would otherwise end up in a landfill, sure, but most plastics can be used again in some way.