Add suggestPositionShot schema types and operation

Mirrors the backend's position-play search: SuggestPositionShotInputGQL
(pot lock + target-area polygon), PositionSuggestionGQL /
PositionShotCandidateGQL / CueStrikeGQL, the Query field, and a
SuggestPositionShot operation with a shared candidate fragment. Rebased
onto master's gql; index.tsx regenerated.

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

src/operations/shot_simulation.gql

@@ -85,3 +85,53 @@ query ComputePotAim(
     occludingBallIds
   }
 }
+
+fragment PositionShotCandidate on PositionShotCandidateGQL {
+  strike {
+    v0
+    phi
+    theta
+    a
+    b
+  }
+  cueFinalPosition
+  inTargetArea
+  distanceToTargetArea
+  robustness
+  potted
+  scratched
+  projection {
+    trajectories {
+      ballId
+      points {
+        time
+        position
+      }
+    }
+    events {
+      eventType
+      time
+      ballIds
+      position
+    }
+    finalState {
+      ballId
+      position
+    }
+    pottedBallIds
+  }
+}
+
+query SuggestPositionShot($suggestionInput: SuggestPositionShotInputGQL!) {
+  suggestPositionShot(suggestionInput: $suggestionInput) {
+    achievable
+    evaluatedCount
+    successfulCount
+    best {
+      ...PositionShotCandidate
+    }
+    alternates {
+      ...PositionShotCandidate
+    }
+  }
+}

src/schema.gql

@@ -81,6 +81,9 @@ type Query {
     targetBallId: Int!
     pocket: PocketIdentifier!
   ): PotAimGQL!
+  suggestPositionShot(
+    suggestionInput: SuggestPositionShotInputGQL!
+  ): PositionSuggestionGQL!
   getOrderedShots(
     filterInput: FilterInput!
     ids: [Int!] = null
@@ -1219,6 +1222,44 @@ type PotAimGQL {
   occludingBallIds: [Int!]!
 }
 
+type PositionSuggestionGQL {
+  achievable: Boolean!
+  best: PositionShotCandidateGQL
+  alternates: [PositionShotCandidateGQL!]!
+  evaluatedCount: Int!
+  successfulCount: Int!
+}
+
+type PositionShotCandidateGQL {
+  strike: CueStrikeGQL!
+  cueFinalPosition: [Float!]!
+  inTargetArea: Boolean!
+  distanceToTargetArea: Float!
+  robustness: Int!
+  potted: Boolean!
+  scratched: Boolean!
+  projection: ShotProjectionGQL
+}
+
+type CueStrikeGQL {
+  v0: Float!
+  phi: Float!
+  theta: Float!
+  a: Float!
+  b: Float!
+}
+
+input SuggestPositionShotInputGQL {
+  cueBallId: Int!
+  targetBallId: Int!
+  pocket: PocketIdentifier!
+  targetArea: [[Float!]!]!
+  balls: [SimulationBallStateInputGQL!] = null
+  b64Image: String = null
+  useHomography: HomographyInputGQL = null
+  tableSize: Float = null
+}
+
 type GetShotsResult {
   shots: [ShotGQL!]!
   count: Int