Answered in detail in the Rust repo.

I need to provide the WATCHOS_DEPLOYMENT_TARGET=9 environment variable when running cargo swift package. It fixes the warnings in the Xcode.

Full command that solves the problem:

WATCHOS_DEPLOYMENT_TARGET=9 cargo run --manifest-path ../../cargo-swift/Cargo.toml swift package -p watchos -n WalletKitV3 -r