Certainly user prompts are a new type of data that could be included in a profile to target users with ads. But note, big tech companies don’t ever want to sell your data. They want to sell your attention, targeted to advertisers by using their proprietary systems on your data. They would prefer to keep the data for themselves and only charge advertisers for attention.
The challengers are going to reshape the tools/interfaces to how data gets created/consumed/evaluated by users. There are more profound shifts afoot than just “more data captured by existing players”. Disruption at the interface layer is the biggest threat. Nostr plays a small role (for now) in this kind of disruption. It could play a larger role over time.