Replace cargo check with cargo clippy on ci

[emilk]

No description provided.

[Copilot]

Pull Request Overview

This PR replaces cargo check commands with cargo clippy in the CI workflow to provide more comprehensive code analysis and linting during continuous integration. The change upgrades the static analysis from basic compilation checks to include clippy's lint warnings.

• Replaced all cargo check commands with cargo clippy equivalents across different target configurations
• Removed redundant step names for consistency, using inline run commands
• Maintained all existing flags and package specifications for each clippy command

---

_{Tip: Customize your code reviews with copilot-instructions.md. Create the file or learn how to get started.}

[github-actions]

Preview available at https://egui-pr-preview.github.io/pr/7581-emilkmore-clippy-on-ci
Note that it might take a couple seconds for the update to show up after the preview_build workflow has completed.