Map the book event game type onto the frontend's vocabulary

[soulrap]

Problem

The whole free spins feature plays on a black screen: no background at all,
base or feature. The scene reappears the instant the round ends.

Background.svelte picks the scene from stateGame.gameType:

const showBaseBackground    = $derived(context.stateGame.gameType === 'basegame');
const showFeatureBackground = $derived(context.stateGame.gameType === 'freeSpins');

bookEventHandlerMap.ts assigns that value straight from the book event:

reveal: async (bookEvent, { bookEvents }) => {
    ...
    stateGame.gameType = bookEvent.gameType;

But the two SDKs do not agree on the vocabulary:

	base	feature
math-sdk — Config in src/config/config.py	basegame	freegame
this app — keys of config.paddingReels, which is what GameType is derived from	basegame	freeSpins

So during a feature round gameType is 'freegame', which matches neither
branch. Both FadeContainers stay hidden and what shows through is the black
Rectangle behind them.

freeSpinTrigger does set the correct value:

stateGame.gameType = 'freeSpins';

…but the next reveal immediately overwrites it. And freeSpinEnd sets
'basegame', which is exactly why the background comes back the moment the
round finishes — the scene that returns is the base one, not the feature one,
so the feature scene is never seen at all.

Measured against the published books for 0_0_scatter:

books_bonus : 4060 reveal events with gameType 'freegame'
books_base  :  400 reveal events with gameType 'basegame'

GameType cannot catch this: the book event is parsed from JSON, so the raw
string flows in untyped.

Change

Map the incoming value onto the frontend's vocabulary at the point of
assignment:

const toGameType = (raw: string): GameType =>
	raw === 'freegame' ? 'freeSpins' : (raw as GameType);

Nothing else changes — freeSpinTrigger and freeSpinEnd already assign the
right literals directly.

Scope

This is not specific to one game. basegame / freegame are the math-sdk
defaults, so any game whose frontend config names the feature freeSpins has
the same silent failure. The other samples in this repo are worth a look; I
only had scatter set up against a live RGS session to confirm it.

If you would rather fix it the other way — rename the config key to freegame
so the two SDKs agree — that works too, but it changes GameType and every
'freeSpins' literal in the app, so I went with the narrower change.