Enable no_std compatibility behind a std feature

[RAprogramm]

Summary

• add an explicit std feature (default) so the crate compiles under no_std + alloc
• refactor the core error types to depend on core/alloc, introduce a CapturedBacktrace alias, and implement AppErrorKind display/error traits manually
• refresh documentation, changelog, and trybuild snapshots for the new surface

Testing

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

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https://chatgpt.com/codex/tasks/task_e_68d49160f12c832ba3fa3fce6760610f