Use AppResult alias across the crate

[RAprogramm]

Summary

• generalize the AppResult type alias to accept alternate error types and document the behavior
• replace remaining Result return types in the frontend helpers with AppResult and update the README example
• update the Actix integration test and docs to leverage AppResult for consistency across the crate

Testing

• cargo +nightly fmt --
• cargo clippy --all-targets --all-features -- -D warnings
• cargo build --all-targets --all-features
• cargo test --all-features
• cargo doc --no-deps --all-features

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https://chatgpt.com/codex/tasks/task_e_68c9fa29f338832b9937e25a7ec080bd