Can personal data be used to train AI models?

Only on the same footing as any other processing, which is harder than it sounds. Training is a purpose in its own right, so it requires consent for that purpose or a recognised legitimate use. Data collected to deliver a service cannot simply be repurposed to train a model without fresh, specific consent. The exemption for data voluntarily made public is narrower than it appears: material scraped broadly from the internet was rarely made public for the purpose of AI training. The point applies with particular force to vendor relationships. A recurring principle across sector guidance is that third parties must not replicate, monetise or make secondary use of personal data without independent consent, and feeding a client's data into a vendor's model to improve that model is secondary use.