ci(rust): parallelize branch checks

[SDAChess]

Summary

Parallelize Rust branch checks and share compiler artifacts more effectively so CI spends less time recompiling the workspace.

Related Issue

No issue required: localized CI workflow and cache maintenance.

Changes

• Split formatting, lockfile validation, linting, tests, build-mode checks, feature aliases, and gateway feature coverage into parallel jobs
• Run test lanes with cargo-nextest and remove redundant bespoke prover and dependency checks
• Add a shared Rust setup action with Nix shell realization, rust-cache, and sccache
• Reuse the Rust setup action when building release binaries

Testing

• mise run pre-commit passes (waived; mise is unavailable locally)
• Unit tests added/updated (not applicable: CI-only change)
• E2E tests added/updated (not applicable: CI-only change)
• actionlint passes for affected workflows
• git diff --check passes
• Nix development shell realization succeeds
• Branch Checks workflow dispatched successfully

Checklist

• Follows Conventional Commits
• Commits are signed off (DCO)
• Architecture docs updated (not applicable)