feat(sidebar): show inbox counts on department cards

[hishboy]

Summary

• add a right-aligned inbox count to each department-card person row
• count pending and fence-archived delivered messages from the existing mailbox read
• refresh cards on mailbox changes without changing pending-only launch demand
• fail closed on mismatched roster/count data and hide, rather than clip, counts in very narrow panes

Tests

• focused inbox tests pass across chiefd-core, chiefd-api, chiefd-host, and chief-cli
• cargo fmt, Clippy, and the macOS compile check pass
• typecheck, package tests, lint, reactive lint, knip, and 99/99 derived pre-push guards pass
• full Rust suite executes all 3,623 expected tests; 3,621 pass and two tmux 3.7c host tests fail identically at the exact base SHA