feat(profile): advertise per-variant dictionary versions for offline preload

The Profile now carries dict_versions (game variant -> current dictionary
version), populated from the dictionary registry at the profileResponse
choke point, so an installed PWA can preload the matching dawg per enabled
variant off the existing cold-start profile request instead of adding a
round-trip for a rare feature.

Wire path: FBS DictVersion table + Profile.dict_versions (additive,
backward-compatible trailing field) -> backend dto/registry -> gateway
ProfileResp + FBS encoder -> client codec decode into a per-variant map on
model.Profile. Empty in a degenerate no-dictionary deployment; the mock
serves v1.3.0 for all three variants. Codec decode covered by a
bite-tested round-trip unit test.

backend/internal/server/banner.go

@@ -8,6 +8,7 @@ import (
 
 	"scrabble/backend/internal/account"
 	"scrabble/backend/internal/ads"
+	"scrabble/backend/internal/engine"
 	"scrabble/backend/internal/notify"
 )
 
@@ -56,9 +57,34 @@ func (s *Server) profileResponse(ctx context.Context, acc account.Account) profi
 	r := profileResponseFor(acc)
 	r.Banner = s.bannerFor(ctx, acc)
 	s.fillLinkedIdentities(ctx, &r, acc.ID)
+	r.DictVersions = s.currentDictVersions()
 	return r
 }
 
+// currentDictVersions reports the current dictionary version of every game variant with a
+// resident dictionary, as engine.Variant stable labels. It backs profileResponse.DictVersions
+// so an offline-capable client preloads the matching dawg per variant off the cold-start
+// profile. A variant without a loaded dictionary is omitted (Registry.Latest reports
+// ErrUnknownVariant); the returned slice is nil only when no variant is resident.
+func (s *Server) currentDictVersions() []dictVersion {
+	if s.registry == nil {
+		return nil // no dictionary registry wired (e.g. a minimal test server): advertise none
+	}
+	variants := []engine.Variant{engine.VariantEnglish, engine.VariantRussianScrabble, engine.VariantErudit}
+	out := make([]dictVersion, 0, len(variants))
+	for _, v := range variants {
+		version, _, err := s.registry.Latest(v)
+		if err != nil {
+			continue
+		}
+		out = append(out, dictVersion{Variant: v.String(), Version: version})
+	}
+	if len(out) == 0 {
+		return nil
+	}
+	return out
+}
+
 // fillLinkedIdentities sets the profile's confirmed email address and platform-linked
 // flags from the account's identities, so the client offers the right link / unlink /
 // change-email controls. A read failure leaves them zero (no controls), logged as a