Port the options screen

OPTION in the start menu runs _Option with the ROM's labels and settings,
OptionsControl's cursor wrapping and each option's bit handling. The four
option bytes live in the script state and saves, defaulting to
DefaultOptions. The battle style now decides whether a trainer's next
Pokémon brings an offer to switch, and the menu account whether the start
menu describes its items; the other settings are kept for later.

Closes #24

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

docs/NATIVE_PORT.md

@@ -35,6 +35,7 @@ These paths refer to the pinned [PRET source](https://github.com/pret/pokecrysta
 | `game/scripts/start-menu.ts`     | `engine/menus/start_menu.asm`, `engine/pokemon/mon_menu.asm`, `mon_submenu.asm`, `party_menu.asm`, `switchpartymons.asm`, `engine/items/pack.asm`, `engine/items/item_effects.asm` | The start menu, the party menu with the Pokémon submenu (STATS, SWITCH, MOVE, ITEM) and the pack (USE, GIVE, TOSS) with the field item effects listed below, including Rare Candy, stones and vitamins. Menu strings, prompts and texts come from the ROM; screens are native. Field moves from the menu (checked by the world), Softboiled and Milk Drink, SEL and the Select button (`SelectMenu`). MAIL and the other field items give a notice. |
 | `game/scripts/pokegear.ts`       | `engine/pokegear/pokegear.asm`, `engine/phone/phone.asm`, `engine/phone/scripts/mom.asm`, `elm.asm`, `engine/rtc/print_hours_mins.asm` | `PokeGear` with each card's joypad handling: the clock (`Pokegear_UpdateClock`, `PrintHoursMins`), the map card's landmark cursor (`TownMap_InitCursorAndPlayerIconPositions`, `TownMap_GetKantoLandmarkLimits`), the phone list (`PokegearPhone_UpdateDisplayList`, `GetCallerClassAndName`, `PokegearPhoneContactSubmenu`, `CheckCanDeletePhoneNumber`) and calls (`MakePhoneCallFromPokegear`, `CheckPhoneContactTimeOfDay`, `GetMapPhoneService`, `HangUp`). Callee scripts run in the event interpreter on the start menu's draft. Screens are native; the radio's stations are not ported. |
 | `game/scripts/trainer-card.ts`   | `engine/menus/trainer_card.asm`, `engine/gfx/player_gfx.asm` (`GetCardPic`), `engine/gfx/cgb_layouts.asm` (`_CGB_TrainerCard`), `home/game_time.asm` | `TrainerCard`'s two reachable pages with their joypad rules, strings from `.Name_Money`, `.Dex_PlayTime` and `.Badges`, the caught count, and the badges from `TrainerCard_JohtoBadgesOAM` with their eight-frame steps. `rendering/trainer-card.ts` draws the card picture, leader faces and badges from the ROM with the card's palettes and attribute map. `world/game-time.ts` is `GameTimer` (capped at 999:59:59). Text is native; the blinking colon's and badges' phase start at the page load. |
+| `game/scripts/options.ts`        | `engine/menus/options_menu.asm`, `data/default_options.asm`, `engine/battle/core.asm` (`CheckWhetherToAskSwitch`), `engine/menus/start_menu.asm` | `_Option` with `OptionsControl` and each option's routine on the four option bytes, `DefaultOptions`, and the two settings consumed so far: `BATTLE_SHIFT` and `MENU_ACCOUNT`. Strings come from the ROM; the screen is native. |
 | `game/scripts/evolution.ts`      | `engine/pokemon/evolve.asm`, `engine/pokemon/learn.asm`, `engine/movie/evolution_animation.asm`, `engine/pokemon/party_menu.asm` | `EvolveAfterBattle`/`EvolvePokemon` over the raw evolution bytes, the evolution texts and a timed, B-stoppable picture sequence, `UpdateSpeciesNameIfNotNicknamed`, `CalcMonStats` and the HP rise, `LearnLevelMoves`, `LearnMove`/`ForgetMove` outside battle and `PlacePartyMonEvoStoneCompatibility`. |
 | `game/rom/pokemon.ts`            | `data/pokemon/base_stats`, `evos_attacks.asm`, `data/moves/moves.asm`, `data/items/attributes.asm`, `engine/gfx/load_pics.asm` | Species, move and item names, base data, evolution lists, learnsets, move PP, item pockets, growth-rate exp and front pictures (`FixPicBank`, `PadFrontpic`). Starter pictures match rebuilt bytes; all 251 evolution lists match the pinned source. |
 | `game/party`                     | `engine/pokemon/move_mon.asm`, `engine/pokemon/caught_data.asm`, `engine/items/items.asm`                                      | `GeneratePartyMonStats` for script gifts: DVs, `FillMoves`, PP, exp, `CalcMonStatC`, happiness and caught data. `PutItemInPocket`, key items and `TossItem`. `SendMonIntoBox`, `SendGetMonIntoFromBox` (deposit and withdraw), `RestorePPOfDepositedPokemon` and `CalcLevel` for the PC's boxes and item storage. TMs and HMs are refused.                                         |
@@ -289,8 +290,8 @@ the original.
 engine flags and the party, and `StartMenu.Items` supplies each item's
 string and description. The start menu runs as `StartMenuRun`, a native
 generator on a copy of the script state, so nothing commits before it
-closes and a save meanwhile keeps the previous state. POKéDEX and OPTION
-are not ported and give a notice; POKéGEAR and the trainer card run inside
+closes and a save meanwhile keeps the previous state. POKéDEX is not
+ported and gives a notice; POKéGEAR, the trainer card and OPTION run inside
 the start menu run.
 
 The party menu prints `PartyMenuStrings` for the `PARTYMENUACTION_*` in use.