You mention "property is theft" which was popularized by Proudhon, but you skip the distinction he clearly makes between personal property (possession in P.'s words) and productive/private property. This conflation of terms is a common misunderstanding of socialism, often used by right wing grifters in statements such as "your toothbrush will be shared". When Proudhon used it, he was referring to the landowner and the capitalist that uses (private) property to steal profits from the laborer, which ironically, you end up defending.
An image generated by a web cartoonist is personal property created by the artist. Like a toothbrush, the owner decides if somebody else can use it and under which conditions. It's not productive property because it has no means of replicating itself and creating new goods. Thus, it's not a target for falling under public/cooperative ownership. Generative AI models are productive property, and are very clearly privately owned in today's society. By using them you are just reinforcing private ownership of means that should be socialized.
Disney, Warner and NYT are perfectly capable of defending their intellectual property in court against AI companies and will end up getting favorable deals (either through reparations, redirection of traffic or removal or copyrighted material). The ones that cannot defend the work that was stolen from them are the small artists that cannot afford prolonged legal battles. By using GenAI, you are not destroying intellectual property, you are just strengthening the companies that currently gain the most from it.
Socialism doesn't just mean "free stuff"; it means equal exchange of labor in the Marxist tradition, and free association of producers in the anarchist tradition (so a producer can choose to not share their creation with you for whatever reason). Usage of GenAI (as it exists today) is incompatible with both.