misc/codex: Directly use install command instead of CARGO_INSTALL_PATH

Using the ports framework's install target (from cargo.mk) with
CARGO_INSTALL_PATH specified seems to run build again, which consumes
too much time, even when the build phase has successfully finished. To
avoid that, use custom do-install target with install command.

While here, remove extraneous binary (logs_client) from installation.

PR: 297995
Reported by: Robert Cina <transitive@gmail.com>
Co-authored-by: Robert Cina <transitive@gmail.com>