refactor(*): DRY up arena scenes, game modes, and HUD instruments

Arenas inherit from a new arena_base.tscn instead of restating ~40 shared
lines each; only sky/ambient/glow/tint/decoration vary, exposed via new
Arena exports since nested Environment properties aren't overridable
through scene inheritance. Bot construction and score-keeping move onto
GameMode, shared by match and spectate modes while preserving their
differing GameSettings-override behavior and the HUD's score-row
duck-typing. HUD instruments share a HudInstrument base for the
smoothing-weight calc and angle-lerp helper. Also dedupes
MAIN_MENU_SCENE_PATH into ScenePaths and documents why DIFFICULTIES
tiers share one checkpoint.

Game/scripts/game_mode.gd

@@ -11,13 +11,18 @@ extends Node3D
 @export var ball_scene: PackedScene = preload("res://objects/ball.tscn")
 
 const CAMERA_RIG_SCENE = preload("res://scenes/ship_camera_rig.tscn")
-const MAIN_MENU_SCENE_PATH = "res://scenes/main_menu.tscn"
 
 var arena: Arena
 var ball: RigidBody3D
 var ships: Array[Ship] = []
 var _ship_spawn_transforms := {}
 
+# Shared by modes that keep score (Match, Spectate); Free Play never
+# references this or emits a score_changed signal, and HUDController relies
+# on has_signal("score_changed") to decide whether to show a score row — so
+# that signal stays declared per-subclass, not here.
+var score := {0: 0, 1: 0}
+
 
 func _ready():
 	# Group lets the HUD discover the game mode for timer/score signals
@@ -97,6 +102,28 @@ func spawn_camera_rig(target: Ship) -> ShipCameraRig:
 	return rig
 
 
+# Given an already-resolved (path, reaction_ticks, action_noise) — callers
+# apply their own GameSettings-override logic first, which differs between
+# modes (Match lets GameSettings override all three fields, Spectate only
+# the path) — builds a trained-policy controller, or an inert placeholder if
+# the path is empty or missing.
+func _build_opponent(model_path: String, reaction_ticks: int, action_noise: float, label: String = "GameMode") -> ShipController:
+	if not model_path.is_empty() and FileAccess.file_exists(model_path):
+		var bot := AIShipController.new()
+		bot.model_path = model_path
+		bot.reaction_ticks = reaction_ticks
+		bot.action_noise = action_noise
+		return bot
+	if not model_path.is_empty():
+		push_warning("%s: bot model not found at %s, spawning inert opponent" % [label, model_path])
+	return ShipController.new()  # inert placeholder
+
+
+func _record_goal(scoring_team: int) -> void:
+	score[scoring_team] += 1
+	print("Goal for team %d! Score: %d - %d" % [scoring_team, score[0], score[1]])
+
+
 # Tiny per-reset randomization, well below anything a player would notice as
 # "not a real kickoff" — just enough that two ships running the identical
 # deterministic AI policy (action_noise = 0) don't start every kickoff from a
@@ -141,4 +168,4 @@ func _reset_body(body: RigidBody3D, to: Transform3D) -> void:
 
 func _unhandled_input(event):
 	if event.is_action_pressed("ui_cancel"):
-		get_tree().change_scene_to_file(MAIN_MENU_SCENE_PATH)
+		get_tree().change_scene_to_file(ScenePaths.MAIN_MENU)