Fix smithy types docs (#3120)

## Motivation and Context
https://docs.rs/crate/aws-smithy-types/0.57.0/builds/954806

Smithy-types docs failed to build.

1. Update CI to run a command more like docs.rs
2. Use auto_doc instead

## Checklist
<!--- If a checkbox below is not applicable, then please DELETE it
rather than leaving it unchecked -->
- [ ] I have updated `CHANGELOG.next.toml` if I made changes to the
smithy-rs codegen or runtime crates
- [ ] I have updated `CHANGELOG.next.toml` if I made changes to the AWS
SDK, generated SDK code, or SDK runtime crates

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