Add Player vs Bot mode with editable tier names

[kenowagb]

Summary

Adds a full Player vs Bot mode that reuses the existing split screen Player vs Player layout, plus a polish pass so bot tier names are editable data and both synthwave floors react to the song.

What players get

• Title tree flow: PLAY then VS Bot then Rookie / Rival / Ace (configurable labels), then the existing Tutorial? stub or song select
• Split screen GameScene with a human on P1 and a rule based bot on P2
• Bot accuracy and reaction delay driven by a ScriptableObject config (no inline rate hardcodes)
• Song select hides the P2 difficulty row; the bot mirrors P1 chart difficulty
• Transition screen and results banner show the chosen bot display name

File guide

Bot core

• Assets/Bot/BotDifficulty.cs: enum tiers (Easy / Medium / Hard / Perfect). Enum names stay stable for serialization; display names live on the config.
• Assets/Bot/BotDifficultySettings.cs: per tier display name, error rate, and decision delay range.
• Assets/Bot/BotDifficultyDefaults.cs: seed and fallback values plus default labels (Rookie / Rival / Ace / Flawless).
• Assets/Bot/BotDifficultyConfig.cs: ScriptableObject table. Gameplay calls GetSettings; UI calls GetDisplayName.
• Assets/Bot/BotPlayerController.cs: decision loop. One roll per tree step, wait for delay and a hittable note, then submit through the same path as a human.
• Assets/Bot/Editor/BotSetupEditorTools.cs: Rhythm menu item to create the config and wire it onto the coordinator and title screen.
• Assets/Bot/Editor/BotDecisionSimulationTests.cs: editor sim for error rate sanity checks.
• Assets/ScriptableObjects/Configs/BotDifficultyConfig.asset: shipped default rates and labels.

Session and integration

• Assets/Session/GameMode.cs: adds PlayerVsBot.
• Assets/Session/GameSession.cs: stores SelectedGameMode, SelectedBotDifficulty, and SelectedBotLabel across scenes.
• Assets/Integration/TreeRhythmController.cs: bot API (OnBotDecisionPoint, GetRequiredAction, HasHittableRhythmNote, SubmitGameplayActionAsync) plus SongAudioSource for shared audio systems.
• Assets/Integration/TwoPlayerGameCoordinator.cs: enables the bot, disables P2 human input, labels results, duplicates P2 synthwave, and wires P1 FFT and beat pulse so the player side background reacts too.
• Assets/Scripts/AudioFFTAnalyzer.cs: SetSource so analysis can follow P1's playing clip (P2 PlaySync never starts audio).
• Assets/Rhythm/Core/RhythmManager.cs: HasHittableNote for bot timing.
• Assets/Tree/Navigation/TreeNavigator.cs: exposes GetRequiredAction for the bot.

Menu and UI

• Assets/Menu/TitleScreen/TitleScreenController.cs: VS Bot node and difficulty sub tree with labels from the config.
• Assets/Menu/SongSelect/*: hide P2 difficulty row in bot mode; transition screen uses SelectedBotLabel.
• Assets/Menu/MenuSceneController.cs: StartTutorial stub hook kept from the original bot commit for the Tutorial? yes path.
• Assets/UI/Style1/ResultScreenController.cs: identity label support for Bot display name.
• Assets/Scenes/GameScene.unity: coordinator bot config wiring.

Docs

• AI/components/PlayerVsBot.md: component doc and file map.
• AI/CHANGELOG.md, AI/COMPONENT_INDEX.md, AI/INDEX.md, TitleScreen / MainMenu doc updates.

Test plan

• Menu: PLAY then VS Bot shows Rookie / Rival / Ace (or renamed labels from the config asset)
• Pick a tier, skip tutorial, pick a song: GameScene loads split screen, P2 acts without human input
• Transition screen and results show the bot display name, not Easy / Medium / Hard
• Both synthwave floors react to the song during the match
• Human 2P still works (no bot spawned)
• 1P still works
• Edit Display Name on BotDifficultyConfig and confirm the title tree updates after re-entering the menu