It may belong to the purchaser however it could still be the manufacturer’s and seller’s responsibility in the case of product liability.
I haven’t reviewed this particular complaint yet so I don’t know which theories of liability are being asserted.
I’m pretty sure the bottles say “please recycle” on them... they also likely have the type of plastic used imprinted, a de facto “warning” about their hazards. If NY is like CA there is a tax paid for single use containers, which can be refunded at least in part to people who return them to recyclers. Unless that money just goes to the state’s general ‘hire more government employees’ fund.
Sure if a company knowingly or through negligence makes a dangerous product they can be held liable (except for covid vaccines) but generally when you buy something the rights to it belong to the purchaser. Hard to imagine what PepsiCo can do to prevent the purchaser from throwing a bottle in the river... especially if it contains a message.