Port the remaining battle items, the stats screen and hBattleTurn at the menu

- Run every non-ball item effect usable in battle from the ROM's
  ItemEffects: Full Restore, revives, bitter medicine, Bitter Berry, Ethers
  and Elixers, X items, X Accuracy, Guard Spec, Dire Hit and Poké Doll.
- Read happiness changes from HappinessChanges, including the larger
  level-up gain where a Pokémon was caught.
- Model hBattleTurn at the battle menu, including the trainer AI's writes,
  and drop the status-heal refusal.
- Port the stats screen for battles and Bill's PC.
- Compare the send-out and withdraw texts, RestoreHealth, RestorePP,
  ChangeHappiness and CalcPlayerStats with the original routines.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

docs/PLAN.md

@@ -130,7 +130,7 @@ The numbered sections below keep their full scope. Each one opens with a checkli
 - Capture with a full party runs `SendMonIntoBox`: the Pokémon goes first in the current box, with restored PP and `SetBoxMonCaughtData`, can be nicknamed and shows `BallSentToPCText`. If the box is already full the ball is not used (`Ball_BoxIsFullMessage`). A catch that fills the box sets `BATTLERESULT_BOX_FULL`; `reloadmapafterbattle` then queues Bill's call (`Script_SpecialBillCall`) as a memory script that runs at the next `PlayerEvents` and is not saved, as in the original.
 - `VAR_BOXSPACE` reads the current box.
 - Save format 3 gained `storage` (boxes, the current box and box names; a null name is the ROM default) and `pcItems`, migrated by absence to empty storage.
-- Not ported: MOVE PKMN W/O MAIL and the stats screen (both show a notice and return to the menu), printing, a `givepoke` with a full party (refused; no open map reaches it) and the tutorial with a full party and box (the original repeats the unusable ball). Changing boxes does not show the save messages; the native session saves continuously.
+- Not ported: MOVE PKMN W/O MAIL (a notice returns to the menu; the stats screen is now ported), printing, a `givepoke` with a full party (refused; no open map reaches it) and the tutorial with a full party and box (the original repeats the unusable ball). Changing boxes does not show the save messages; the native session saves continuously.
 - Next: the introduction's naming and clock screens, player switching and other items in battle, then party and bag menus.
 
 ## Implemented: the introduction's naming and clock screens
@@ -144,7 +144,7 @@ The numbered sections below keep their full scope. Each one opens with a checkli
 - Save format 3 gained `intro` and `clock.minuteOffset`, migrated by absence to a finished intro on the device clock.
 - Intentional change: the steppers start at the device's current time rather than 10:00, so confirming keeps the device clock.
 - Not presented: the palette fades, Wooper's cry, the picture slide during name selection, `ShrinkPlayer` and the Route 30 music (no audio yet).
-- Next: MOVE PKMN W/O MAIL and the stats screen with the party menu.
+- Next: MOVE PKMN W/O MAIL with the party menu.
 
 ## Implemented: evolution data, reference vectors and the opening playthrough
 
@@ -152,15 +152,19 @@ The numbered sections below keep their full scope. Each one opens with a checkli
 - The reference suite also runs the original `CalcMonStats` (300 cases, with and without stat experience, including levels above 100 that reach the 999 cap) and `CalcExpAtLevel` (every growth rate at levels 1–100).
 - `tests/playthrough.test.ts` plays a new game from the introduction to the catching tutorial with a seeded RNG: Mom, Elm, the starter and Potion, Route 29, Cherrygrove, Route 30, Mr. Pokémon, Elm's call, the rival battle, the officer, the Egg, the aide's Poké Balls and the Dude's demonstration. Wild battles are fought, or fled below half HP. Each stage ends with a JSON save loaded into a fresh world. It uses no fixtures or hand-set flags, but drives `GameWorld` directly rather than the browser UI.
 
-## Implemented: switching and healing items in battle
+## Implemented: switching, battle items and the stats screen
 
-- PKMN opens the party menu; SWITCH sends out the chosen Pokémon (STATS is not ported). The texts, the trapped and fainted checks, and the enemy's turn after the switch follow the original. Both Pokémon share the experience.
+- PKMN opens the party menu; SWITCH sends out the chosen Pokémon and STATS opens the stats screen. The texts, the trapped and fainted checks, and the enemy's turn after the switch follow the original. Both Pokémon share the experience.
 - After a faint, wild battles ask "Use next POKéMON?" (NO tries to run) and the party menu cannot be cancelled. Trainers' next Pokémon come with Shift mode's offer to switch; a double faint sends out both sides.
-- PACK's Items pocket uses HP items (Potion, Berry and the rest of `HealingHPAmounts`) and status healers (Antidote, Parlyz Heal, Awakening, PSNCUREBERRY and the rest of `StatusHealingActions`) on any party Pokémon. Items with no battle use get Oak's warning. X items, Poké Doll, Full Restore and revives are refused.
+- PACK's Items pocket uses HP items (Potion, Berry and the rest of `HealingHPAmounts`) and status healers (Antidote, Parlyz Heal, Awakening, PSNCUREBERRY and the rest of `StatusHealingActions`) on any party Pokémon. Items with no battle use get Oak's warning.
+- Every other battle item effect runs too: Full Restore, revives, the bitter herbs, Bitter Berry, Ethers and Elixers, X items, X Accuracy, Guard Spec, Dire Hit and Poké Doll. Happiness changes come from the ROM's `HappinessChanges`.
+- `hBattleTurn` at the battle menu is modelled, so `CalcPlayerStats` after a status heal penalises the side the original does.
+- The stats screen shows its three pages from BattleMonMenu and Bill's PC.
+- The reference suite compares the send-out and withdraw texts, `RestoreHealth`, `RestorePP`, `ChangeHappiness` and `CalcPlayerStats` with the original routines.
 
 ## Native battles: current state
 
-The battle core, ROM tables, encounter hooks, battle UI and whiteout hooks are present. Unit tests cover wins, escape, loss, experience, move learning and capture; reference tests compare damage, type effectiveness, stat calculation and experience curves. Browser tests drive a test-only wild encounter through the real UI: victory with level-up and move learning, escape, whiteout, catching with a nickname, keyboard and on-screen D-pad menu navigation, mid-battle backup restore, rollback of unsupported effects, switching through the party menu and a Potion from the Items pocket. Real Route 29 encounters now use the ROM's encounter tables. Other battle items (X items, Poké Doll, Full Restore, revives) remain unfinished.
+The battle core, ROM tables, encounter hooks, battle UI and whiteout hooks are present. Unit tests cover wins, escape, loss, experience, move learning and capture; reference tests compare damage, type effectiveness, stat calculation and experience curves. Browser tests drive a test-only wild encounter through the real UI: victory with level-up and move learning, escape, whiteout, catching with a nickname, keyboard and on-screen D-pad menu navigation, mid-battle backup restore, rollback of unsupported effects, switching through the party menu and a Potion from the Items pocket. Real Route 29 encounters now use the ROM's encounter tables. Only the special Kurt and Park balls remain unported among battle items.
 
 This is still not a complete new game. Full party/bag/Pokégear menus, story progression beyond Route 30 and Mr. Pokémon's house, and audio remain unfinished. The Key Items menu supports the Bicycle; the PCs store Pokémon, items and decorations. Surfing and terrain animation now have native implementations; later maps remain gated. Save slots, a Johto/Kanto atlas, Pokédex records, online Link, friends and real-world steps come later.
 
@@ -228,7 +232,7 @@ their scripts and story progression are supported.
 - [x] The Cherrygrove rival battle, Elm's call and the return to Elm
 - [x] Capture and the catching tutorial
 - [x] Battles: stats, damage, types, accuracy, criticals, status, turn order, fainting, experience, move learning, trainer AI, trainer send-outs and prize money
-- [x] Player switching, and HP and status healing items, in battle (X items, Poké Doll, Full Restore and revives are refused)
+- [x] Player switching and every non-ball battle item, with the stats screen
 - [x] The PC and boxes (catching with a full party)
 - [x] The introduction's naming and clock screens
 - [ ] Controlled-seed comparisons with the original for random-driven routines (accuracy, criticals, damage variation, capture). Damage, types, stats and experience curves are compared.