The native PR introduced tokio-tungstenite and reqwest with native-tls,
which depends on openssl-sys (C library). This breaks the release
workflow's cargo-zigbuild cross-compilation on Linux because zig's C
compiler can't find the system OpenSSL headers.
Switch to rustls (pure Rust TLS) which has zero C dependencies and
cross-compiles trivially. Also shrinks the dependency tree.