air travel – Can an airline, such as Iberia, see my recent flight history with Vueling?

Hard to know for sure, but quite likely the answer is yes. Both airlines are owned by the same parent company and are likely sharing some of the backend infrastructure.

Iberia has certainly access to some data about a code share flight but it’s hard to say if that also includes the full passenger list even if Vueling sold the ticket.

So the answer to “can they” is probably “yes”. That doesn’t man that they “will” or if it’s legal for them to do so. For the latter, you would have to read the terms and conditions of both tickets (and that you agreed to) and also read the contract of carriage of both airlines.