[codecane] copy over NEXT_PUBLIC_* envs #479

Job	Run time
prepare-and-commit-staging	42s
build-staging-binaries / build-windows-binary	2m 36s
build-staging-binaries / build-binaries (ubuntu-latest, linux-x64, bun-linux-x64, linux, x64)	1m 20s
build-staging-binaries / build-binaries (ubuntu-latest, linux-arm64, bun-linux-arm64, linux, arm64, false)	1m 16s
build-staging-binaries / build-binaries (macos-14, darwin-arm64, bun-darwin-arm64, darwin, arm64)	1m 23s
build-staging-binaries / build-binaries (macos-13, darwin-x64, bun-darwin-x64, darwin, x64)	3m 16s
create-staging-release	19s
publish-staging-npm	15s
	11m 7s

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