By purchasing oil to turn into plastics, manufacturers are in competition with buyers who intend to simply burn their oil-derived products (fuels). This increased competition must cause some (small) increase in the price of oil that has to be paid by the oil burners, making it marginally less economically competitive in comparison to renewable energy sources.
The effect might be negligible, and I obviously haven't modelled whether this leads to a significant reduction in oil burning (especially relative to the carbon pollution of the container ships, as you say), but it is an interesting thought experiment.
but...
The oil isn't turned into plastic[0], the petrochemicals used in plastic don't compete with fuel, it is a byproduct of the oil extraction and fracturing process[1] mostly from the lighter natural gas components I believe. The effect is likely the opposite of what you imagine it to be in your example.
Keep in mind that the price of fuel isn't the same as the price of crude, as the fuel is a separate commodity whose production is tied to refinement of crude, which is the primary commodity.
In fact, using this industrial byproduct to create plastic will reduce the cost of oil extraction. The transportation of the packaged good which are enabled by this ubiquitous packaging technology will now drive demand for transportation, in turn raising the price again. The cheapening of fuel and plastic packaged goods incentivizes further usage and investment, and so the wheels turn on ...
It gets much more complicated from there and also involves some missiles and ground-based radar systems.
[0] - https://inbound.teamppi.com/blog/oil-to-plastic-a-lesson-on-...
So no, I am not saying that.