R6(a): de-stage code, docs, READMEs; split stage6_test

Mechanical, behaviour-preserving removal of Stage N / TODO-N / phase (RN)
references from comments, doc-comments, service READMEs, the current-state docs
(ARCHITECTURE, FUNCTIONAL+_ru, TESTING, UI_DESIGN), config-file comments, and the
.fbs/.proto schema comments. PLAN.md / PRERELEASE.md / CLAUDE.md keep the stage
history.

- Rename the only stage-named identifiers: registerStage8 -> registerSocialOps,
  registerStage11 -> registerLinkOps (gateway transcode).
- Split stage6_test.go: TestEmailLoginFlow -> email_test.go,
  TestGuestAutoMatchLeavesNoStats (+ provisionGuest) -> account_test.go.
- Regenerated proto bindings (push.pb.go, telegram_grpc.pb.go) from the de-staged
  .proto comments; FB Go/TS bindings unchanged (flatc strips schema comments).

go build/vet/gofmt clean across modules; integration typecheck and pnpm check green.

backend/internal/server/handlers_game.go

@@ -12,10 +12,9 @@ import (
 	"scrabble/backend/internal/game"
 )
 
-// The handlers below extend the Stage 6 vertical slice with the remaining game and
-// chat operations the UI needs (PLAN.md Stage 7). They follow the same pattern as
-// handlers_user.go: X-User-ID identity, the domain service call, a JSON DTO mapped
-// from the result.
+// The handlers below cover the game and chat operations the UI needs. They follow
+// the same pattern as handlers_user.go: X-User-ID identity, the domain service
+// call, a JSON DTO mapped from the result.
 
 // hintResultDTO is the top-ranked move plus the remaining hint budget.
 type hintResultDTO struct {
@@ -53,7 +52,7 @@ type chatListDTO struct {
 }
 
 // exchangeRequest swaps the given rack tiles back into the bag. Tiles are wire alphabet
-// indices (Stage 13); a blank is engine.BlankIndex.
+// indices; a blank is engine.BlankIndex.
 type exchangeRequest struct {
 	Tiles []int `json:"tiles"`
 }
@@ -211,7 +210,7 @@ func (s *Server) handleEvaluate(c *gin.Context) {
 }
 
 // handleCheckWord looks a word up in the game's pinned dictionary. The word arrives as
-// repeated ?idx= alphabet indices (Stage 13); the backend decodes them to the concrete
+// repeated ?idx= alphabet indices; the backend decodes them to the concrete
 // word for the lookup and echoes that concrete word back for the client's result cache.
 func (s *Server) handleCheckWord(c *gin.Context) {
 	_, gameID, ok := s.userGame(c)
@@ -242,7 +241,7 @@ func (s *Server) handleCheckWord(c *gin.Context) {
 }
 
 // queryIndexes parses repeated integer query parameters (e.g. ?idx=2&idx=0) into a slice.
-// It carries a word-check query as alphabet indices on a GET (Stage 13).
+// It carries a word-check query as alphabet indices on a GET.
 func queryIndexes(c *gin.Context, key string) ([]int, error) {
 	raw := c.QueryArray(key)
 	out := make([]int, 0, len(raw))
@@ -326,7 +325,7 @@ type draftTileDTO struct {
 	Blank  bool   `json:"blank"`
 }
 
-// draftDTO is a player's persisted client-side composition for a game (Stage 17): the
+// draftDTO is a player's persisted client-side composition for a game: the
 // preferred rack tile order (an opaque client string) and the board tiles laid but not yet
 // submitted. The gateway forwards the JSON verbatim; this layer owns its shape.
 type draftDTO struct {
@@ -352,7 +351,7 @@ func (d draftDTO) toDomain() game.Draft {
 	return game.Draft{RackOrder: d.RackOrder, BoardTiles: tiles}
 }
 
-// handleGetDraft returns the player's saved composition for a game (Stage 17), or an empty
+// handleGetDraft returns the player's saved composition for a game, or an empty
 // draft when none is stored.
 func (s *Server) handleGetDraft(c *gin.Context) {
 	uid, gameID, ok := s.userGame(c)
@@ -367,7 +366,7 @@ func (s *Server) handleGetDraft(c *gin.Context) {
 	c.JSON(http.StatusOK, draftDTOFrom(d))
 }
 
-// handleSaveDraft upserts the player's composition for a game (Stage 17). The service
+// handleSaveDraft upserts the player's composition for a game. The service
 // rejects a non-player with ErrNotAPlayer.
 func (s *Server) handleSaveDraft(c *gin.Context) {
 	uid, gameID, ok := s.userGame(c)