I've got a book for you to read...

https://en.wikipedia.org/wiki/The_medium_is_the_message

If I have trillions of monkeys on typewriters generating every possible combination of characters, and then from what they "produce" I carefully select what I want to show everyone who comes to my website, how responsible am I for what my visitors see?

they pay people to create content for their platform, and use their editorial control to determine what gets surfaced for you to see.

how is that not "producing content"?

No, but they decide the moderation policy that incentivizes the content produced (by nature of selecting which users feel comfortable using their product and which do not).

For example, I do not feel comfortable using the same platform as people that post child sexual abuse material. X's Grok is infamous for generating such content on demand. I opt to use platforms that do not have this as a first-class feature. X has selected against my participation and for the participations of people who hold a contrary opinion to me. Even if Grok stops producing CSAM, that selection bias will persist.

And yet people struggle to get Elon Musk out of their feeds on Twitter.