feat(game): add GET /{gameId}/fen-history endpoint

Returns a FEN string for every ply of the game (initial position + one
per move) by replaying moves via ruleSet.applyMove and exporting each
GameContext to FEN. Enables full per-move engine analysis from clients
without requiring a chess library on their side.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

modules/api/src/main/scala/de/nowchess/api/dto/FenHistoryDto.scala

@@ -0,0 +1,3 @@
+package de.nowchess.api.dto
+
+final case class FenHistoryDto(fens: List[String])

modules/core/src/main/scala/de/nowchess/chess/resource/GameResource.scala

@@ -339,6 +339,18 @@ class GameResource:
     log.infof("Imported PGN game %s", entry.gameId)
     created(GameDtoMapper.toGameFullDto(entry, ioClient))
 
+  @GET
+  @Path("/{gameId}/fen-history")
+  @Produces(Array(MediaType.APPLICATION_JSON))
+  def getFenHistory(@PathParam("gameId") gameId: String): Response =
+    val entry   = registry.get(gameId).getOrElse(throw GameNotFoundException(gameId))
+    val engine  = entry.engine
+    val initial = engine.initialContext
+    val moves   = engine.context.moves
+    val contexts = moves.scanLeft(initial)((ctx, move) => engine.ruleSet.applyMove(ctx)(move))
+    val fens     = contexts.map(ctx => ioClient.exportFen(ctx))
+    ok(FenHistoryDto(fens))
+
   @GET
   @Path("/{gameId}/export/fen")
   @Produces(Array(MediaType.TEXT_PLAIN))