Implement #160, #161, #162, #163, #164 and #165

#162 - a single tap bought a research node outright. One physical tap arrives
TWICE: Godot emulates a mouse button from every touch AND a touch from every
mouse button, both project settings are on, and the menu's dispatcher routes
InputEventScreenTouch and InputEventMouseButton alike to the tree. The second
arrival found the node already selected and took itself for the confirming
tap. Measured, not reasoned about - one tap produced two picks and two
confirms.

What is ignored is specifically the TWIN: same frame, same place, arriving
through the other input kind. Deduping on frame and position alone also
swallowed two genuine taps in one frame, which the test caught.

#164 - the build menu predicted a caption's height from the COLUMN WIDTH:
wide column, assume one line. Right for most names and wrong for the long
ones, so "Spacial Workshop" wrapped onto the price beneath it. Captions are
now measured against the font that draws them, and prices sized from
PriceTag.wanted_height(), which existed for exactly this and was not being
asked. Prices are set before anything is measured, because the old order laid
out first and priced afterwards.

The ship lab: its buy button is gone and a second tap on an option buys it,
the same rule as the research tree; the explanation drops into the room that
freed; research points move up into the resource table, where everything else
being spent already is; the second row of options is placed from the first
row's measured bottom rather than a constant; and the vessel strip is spaced
from the panel's own width, so the eighth vessel is no longer half off the
right edge.

#160 - the quest panel was drawn BEFORE the sticks and the pivot pair, so
they sat on top of it. Moved after them, under the narration banner. Its title
rule ran straight through the close button; the header band is now as tall as
that button.

#161 - the prologue widens the formation into a freight convoy by writing over
GameState.formation, and nothing put it back. The player flew the convoy's
600-unit spread for the rest of the game - a shape nobody chose, which reads
as the fleet having drifted apart.

#163 - a quest to station a vessel at the outpost, after the one that asks for
the outpost. Building one and crewing it are different acts, and an empty
outpost holds nothing.

#165 - the gas bomb's blast and a vessel arriving fast both damage a
structure. The blast used to stop politely at anything the player owned, which
made a bomb dropped on a besieged mothership a free way to sweep the attackers
off it.

Collisions are caught on ENTRY, not on the 0.7s strike tick: a vessel is only
moving fast for the instant it arrives, and a ship sent in at 900 did no
damage at all until this moved. Docking is free - the fleet sits on its own
mothership constantly to bank ore - and garrison vessels are exempt outright,
because they launch from their outpost and re-dock with it at speed. The suite
caught that one: the ram rule was destroying the garrison as it launched.

Suite 153/153. Four tests changed because what they pinned moved: the lab's
buy button, the intro's formation, the research tree's tap delivery, and the
build menu's own preview.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

ui/SkillTreeView.gd

@@ -53,6 +53,25 @@ const WHEEL_STEP: float = 90.0
 # the second one is never a blind commitment.
 signal node_confirmed(id: String)
 
+# One physical tap arrives TWICE. Godot emulates a mouse button from every
+# touch and a touch from every mouse button - both settings are on - and the
+# menu's dispatcher routes InputEventScreenTouch and InputEventMouseButton
+# here alike. The second arrival found the node already selected and took it
+# for the confirming tap, so a single tap bought the research outright: the
+# exact thing the two-tap rule exists to prevent (#162). Measured, not
+# guessed - one tap produced two picks and two confirms.
+#
+# What is ignored is specifically the TWIN: a press at the same place, in the
+# same frame, arriving through the OTHER input kind. Two presses of the same
+# kind are always two taps however close together they are, so a player
+# tapping twice quickly is never swallowed. Deduping on frame and position
+# alone did swallow it, which the test caught.
+enum PressSource { TOUCH, MOUSE }
+
+var _last_press_frame: int = -1
+var _last_press_at: Vector2 = Vector2.ZERO
+var _last_press_source: int = -1
+
 var selected_id: String = ""
 var scroll_y: float = 0.0
 var _dragging: bool = false
@@ -144,7 +163,7 @@ func _state_color(node: Dictionary) -> Color:
 # Returns true when the press landed on a node, so the caller knows the
 # touch was consumed.
 func handle_touch(event: InputEventScreenTouch) -> bool:
-	return handle_press(event.pressed, event.position)
+	return handle_press(event.pressed, event.position, PressSource.TOUCH)
 
 
 func handle_drag(event: InputEventScreenDrag) -> bool:
@@ -160,7 +179,7 @@ func handle_mouse_button(event: InputEventMouseButton) -> bool:
 		return handle_pan(Vector2(0.0, -WHEEL_STEP))
 	if event.button_index != MOUSE_BUTTON_LEFT:
 		return false
-	return handle_press(event.pressed, event.position)
+	return handle_press(event.pressed, event.position, PressSource.MOUSE)
 
 
 # Only while the button is held. A touch drag cannot arrive without a finger
@@ -173,12 +192,14 @@ func handle_mouse_motion(event: InputEventMouseMotion) -> bool:
 	return handle_pan(event.relative)
 
 
-func handle_press(pressed: bool, at: Vector2) -> bool:
+func handle_press(pressed: bool, at: Vector2, source: int = PressSource.TOUCH) -> bool:
 	if not visible:
 		return false
 	if not pressed:
 		_dragging = false
 		return true
+	if _is_emulated_twin(at, source):
+		return true
 	_dragging = true
 	var local: Vector2 = at - global_position
 	for node in GameState.SKILL_TREE:
@@ -193,6 +214,20 @@ func handle_press(pressed: bool, at: Vector2) -> bool:
 	return false
 
 
+# True only for the emulated twin: same frame, same place, other input kind.
+func _is_emulated_twin(at: Vector2, source: int) -> bool:
+	var frame: int = Engine.get_process_frames()
+	var twin: bool = frame == _last_press_frame \
+		and source != _last_press_source \
+		and at.distance_to(_last_press_at) < 24.0
+	if twin:
+		return true
+	_last_press_frame = frame
+	_last_press_at = at
+	_last_press_source = source
+	return false
+
+
 func handle_pan(relative: Vector2) -> bool:
 	if not visible:
 		return false