refactor: rely on auto Send/Sync for DbInner

[belveryin]

Summary

• Remove manual unsafe impl Send/Sync for DbInner so auto-trait checks enforce thread-safety based on fields.
• Let the compiler catch non-Send/Sync additions instead of masking them.

Testing

• cargo +nightly fmt --all -- --check
• cargo clippy --workspace -- -D warnings
• cargo build --verbose
• cargo test --verbose
• cargo llvm-cov --workspace --lcov --output-path target/coverage/lcov.info --fail-under-lines 80
• cargo test public_api_e2e:: -- --nocapture

[ethe]

I'm not sure if this can be compiled on WASM, I'd like to fix ci trigger firstly and then check it