An waste industry buddy of mine designs landfills, and this is his take too. It's better to throw your plastic into regular trash (and other recyclables into the recycle bin), because then you at least know it's likely to end up in a landfill where it's safe, instead of being exported and dumped in the sea.
Most modern landfills have power stations that burn off these gases for electricity or heat for local consumption.
The ones that don't can be GHG emitters, but that just means there are less emissions somewhere else (where trash was collected from), because you just concentrated a bunch of matter in one place. It's not a significant net emitter.
Which is why it pains me so much that my municipality doesn't include (at least a household food scrap sized) compost bin with standard garbage service. They only offer a giant and expensive yard-waste bin.
That's why I mentioned long term, as you expand the time horizon you consider it over, landfill for plastics gets worse as it starts to decompose compared with incinerating with energy recovery or recycling.
Define long-term? I think that, as you expand the time horizon, you'll first reach the point at which the landfill gets buried, effectively sequestering the plastics and the carbon within.
An waste industry buddy of mine designs landfills, and this is his take too. It's better to throw your plastic into regular trash (and other recyclables into the recycle bin), because then you at least know it's likely to end up in a landfill where it's safe, instead of being exported and dumped in the sea.