They do

https://platform.claude.com/docs/en/build-with-claude/struct...

> Structured outputs are generally available on the Claude API for Claude Opus 4.8, Claude Mythos Preview, Claude Opus 4.7, Claude Opus 4.6, Claude Sonnet 4.6, Claude Sonnet 4.5, Claude Opus 4.5, and Claude Haiku 4.5