feat(doctor): battery health readout (#80)

Report-only cycle_count + retained capacity (charge_* or energy_*) as
% of design on system batteries; soft warn below 70% of design; skip
when attrs missing. NOMARCHY_POWER_SUPPLY_ROOT for the checks.doctor
fixture (test_power has no cycle/design attrs).

Verified: V2 — nix flake check --no-build; checks.doctor green (fake
BAT0 cycles/% + Device-scope ignore); local BAT0 smoke (energy_*).

pkgs/nomarchy-doctor/nomarchy-doctor.sh

@@ -263,6 +263,61 @@ if [ "$bat_seen" -eq 1 ] && [ "$bat_limited" -eq 0 ]; then
   skip "battery charge limit (none set — charges to 100%)"
 fi
 
+# ── battery health (report-only, BACKLOG #80) ────────────────────────
+# cycle_count + retained capacity (charge_* µAh or energy_* µWh). Same
+# system-battery filter as charge-limit/notify. Self-gates when no
+# battery or the firmware omits the attrs (desktops, bare VMs). Override
+# the sysfs root with NOMARCHY_POWER_SUPPLY_ROOT for the checks.doctor
+# fixture (test_power has no cycle/design attrs).
+ps_root="${NOMARCHY_POWER_SUPPLY_ROOT:-/sys/class/power_supply}"
+bat_health_seen=0
+for bat in "$ps_root"/*/; do
+  [ -d "$bat" ] || continue
+  [ "$(cat "$bat/type" 2>/dev/null)" = Battery ] || continue
+  [ "$(cat "$bat/scope" 2>/dev/null || echo System)" = Device ] && continue
+  name=$(basename "$bat")
+
+  cycles=$(cat "$bat/cycle_count" 2>/dev/null || true)
+  case "$cycles" in ''|*[!0-9]*) cycles= ;; esac
+  # Some firmwares export 0 forever — treat as unknown, not "brand new".
+  if [ -n "$cycles" ] && [ "$cycles" -eq 0 ]; then cycles=; fi
+
+  full=""; design=""
+  if [ -r "$bat/charge_full" ] && [ -r "$bat/charge_full_design" ]; then
+    full=$(cat "$bat/charge_full" 2>/dev/null || true)
+    design=$(cat "$bat/charge_full_design" 2>/dev/null || true)
+  elif [ -r "$bat/energy_full" ] && [ -r "$bat/energy_full_design" ]; then
+    full=$(cat "$bat/energy_full" 2>/dev/null || true)
+    design=$(cat "$bat/energy_full_design" 2>/dev/null || true)
+  fi
+  case "$full" in ''|*[!0-9]*) full= ;; esac
+  case "$design" in ''|*[!0-9]*) design= ;; esac
+  pct=""
+  if [ -n "$full" ] && [ -n "$design" ] && [ "$design" -gt 0 ]; then
+    pct=$(( full * 100 / design ))
+  fi
+
+  [ -n "$cycles" ] || [ -n "$pct" ] || continue
+  bat_health_seen=1
+
+  detail=""
+  [ -n "$cycles" ] && detail="${cycles} cycles"
+  if [ -n "$pct" ]; then
+    [ -n "$detail" ] && detail="$detail, "
+    detail="${detail}${pct}% of design capacity"
+  fi
+  # Soft warn only — wear isn't a doctor "fix", just a heads-up.
+  if [ -n "$pct" ] && [ "$pct" -lt 70 ]; then
+    warn "$name health: $detail" \
+         "battery wear is normal over years — replace when runtime suffers"
+  else
+    ok "$name health: $detail"
+  fi
+done
+if [ "$bat_health_seen" -eq 0 ]; then
+  skip "battery health (no system battery / no cycle or design capacity attrs)"
+fi
+
 # ── hibernate / sleep (BACKLOG #76) ──────────────────────────────────
 # Read-only: is there a working hibernate path? zram is RAM-only and can't
 # hold a resume image, so hibernation needs a disk swap (partition or file)