Improve integration testing (file organization, time, memory)

[FabijanC]

Usage related changes

None, hopefully.

Development related changes

• Move integration tests into a separate crate tests/integration:
  • According to https://matklad.github.io/2021/02/27/delete-cargo-integration-tests.html
  • Modified the publishing shell script to skip that crate
• Close Unused import warnings #624
• Use --all-targets with clippy
• Remove unused bench
• Separate testing code from production code

Checklist:

• Checked out the contribution guidelines
• Applied formatting - ./scripts/format.sh
• No linter errors - ./scripts/clippy_check.sh
• No unused dependencies - ./scripts/check_unused_deps.sh
• No spelling errors - ./scripts/check_spelling.sh
• Performed code self-review
• Rebased to the latest commit of the target branch (or merged it into my branch)
  • Once you make the PR reviewable, please avoid force-pushing
• Updated the docs if needed - ./website/README.md
• Linked the issues resolvable by this PR - linking info
• Updated the tests if needed; all passing - execution info

[FabijanC]

Currently experiencing race condition in tests. #666 should resolve the issue.