Of course, generating fuels from plastic that you create from oil is still transferring fossil deposited carbon straight into our atmosphere. Euphemistically labeling that as a bio fuel does not change that and is more than a bit disingenuous/misleading. And probably intentionally so by those advocating this.
There's nothing green or climate friendly about this. Dumping it a landfill is literally better for the environment because at least then the carbon goes back into the ground. Of course you do get some local pollution with that. So, it's not a perfect strategy. Incineration with carbon capture might be feasible but is probably going to be expensive.
Of course getting rid of a lot of single use plastics is better still. The best carbon capture strategy is simply leaving it in the ground and not messing around with it.