Those cardboard tubs will have a plastic liner and thus be un-recyclable and non-compostable. Nearly no consumer cardboard containers for non-dry food are pure

Those cardboard tubs will have a plastic liner and thus be un-recyclable and non-compostable. Nearly no consumer cardboard containers for non-dry food are pure cardboard, they all have liners to protect the cardboard. Very few will have a wax lining but that is the legacy method and more expensive than plastic so they are few and far between. The litmus test is does the packaging begin to break down after 10 or so minutes holding wet food, if yes then the packaging is likely just paper, i.e. cardboard, if it can sit in a fridge for 48 hours without issue it has plastic.