Replace Nix flake with mise for toolchain management, treefmt for
formatting, prek for pre-commit hooks, and a Dockerfile for container
builds. Update CI workflows to use jdx/mise-action instead of Nix.
Add system dependency instructions to README.md and CLAUDE.md.
Merge separate lint and test jobs into a single check job so clippy's
compilation artifacts are reused by tests. Add actions/cache for the
Cargo target directory and registry to enable incremental builds across
runs. Drop unnecessary fetch-depth: 0 from CI jobs.