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/dto.go

@@ -63,6 +63,20 @@ type profileResponse struct {
 	Email          string `json:"email"`
 	TelegramLinked bool   `json:"telegram_linked"`
 	VkLinked       bool   `json:"vk_linked"`
+	// DictVersions lists the current dictionary version per game variant (engine.Variant
+	// stable labels). An installed PWA preparing for offline play reads it to preload the
+	// right dawg per enabled variant off this cold-start response, without an extra request.
+	// Filled outside the pure projection (it reads the dictionary registry), so it is empty
+	// for callers that build the DTO without a Server. See Server.profileResponse.
+	DictVersions []dictVersion `json:"dict_versions,omitempty"`
+}
+
+// dictVersion pairs a game variant's stable label (engine.Variant.String) with its current
+// dictionary version. profileResponse.DictVersions carries the set so an offline-capable
+// client preloads the matching dawg per variant.
+type dictVersion struct {
+	Variant string `json:"variant"`
+	Version string `json:"version"`
 }
 
 // tileDTO is one placed (or to-place) tile.