The Postgres TEXT type is limited to 65,535 bytes, to give a concrete number. "Big" usually means, big enough that you have to stream rather than sending all at once.
You're right. Bad Google suggestion for "max string length postgres" that pointed to https://hevodata.com/learn/postgresql-varchar/ saying varchar max is 64KB, which is also wrong. I gotta stick to the official docs. Anyway, TEXT is the one we care about.