feat: add single player snake mode

Add solo mode where players survive as long as possible while tracking
score (food eaten). Single player games start with a shorter 3-second
countdown vs 10 seconds for multiplayer, maintain exactly 1 food item
for classic snake feel, and end when the player dies rather than when
one player remains.

- Add GameMode type (ModeMultiplayer/ModeSinglePlayer) and Score field
- Filter single player games from "Join a Game" lobby list
- Show "Ready?" and "Score: X" UI for single player mode
- Hide invite link for single player games
- Preserve game mode on rematch

ui/snakelobby.go

@@ -7,14 +7,32 @@ import (
 	"github.com/ryanhamamura/via/h"
 )
 
-func SnakeLobbyTab(nicknameBind h.H, presetClicks []h.H, activeGames []*snake.SnakeGame) h.H {
-	var presetButtons []h.H
+func SnakeLobbyTab(nicknameBind h.H, soloClicks, multiClicks []h.H, activeGames []*snake.SnakeGame) h.H {
+	// Solo play buttons
+	var soloButtons []h.H
 	for i, preset := range snake.GridPresets {
 		var click h.H
-		if i < len(presetClicks) {
-			click = presetClicks[i]
+		if i < len(soloClicks) {
+			click = soloClicks[i]
 		}
-		presetButtons = append(presetButtons,
+		soloButtons = append(soloButtons,
+			h.Button(
+				h.Class("btn btn-secondary"),
+				h.Type("button"),
+				h.Text(fmt.Sprintf("%s (%d×%d)", preset.Name, preset.Width, preset.Height)),
+				click,
+			),
+		)
+	}
+
+	// Multiplayer buttons
+	var multiButtons []h.H
+	for i, preset := range snake.GridPresets {
+		var click h.H
+		if i < len(multiClicks) {
+			click = multiClicks[i]
+		}
+		multiButtons = append(multiButtons,
 			h.Button(
 				h.Class("btn btn-primary"),
 				h.Type("button"),
@@ -24,22 +42,28 @@ func SnakeLobbyTab(nicknameBind h.H, presetClicks []h.H, activeGames []*snake.Sn
 		)
 	}
 
-	createSection := h.Div(h.Class("mb-6"),
-		h.H3(h.Class("text-lg font-bold mb-2"), h.Text("Create Game")),
-		h.Div(h.Class("mb-4"),
-			h.FieldSet(h.Class("fieldset"),
-				h.Label(h.Class("label"), h.Text("Your Nickname"), h.Attr("for", "snake-nickname")),
-				h.Input(
-					h.Class("input input-bordered w-full"),
-					h.ID("snake-nickname"),
-					h.Type("text"),
-					h.Placeholder("Enter your nickname"),
-					nicknameBind,
-					h.Attr("required"),
-				),
+	nicknameField := h.Div(h.Class("mb-4"),
+		h.FieldSet(h.Class("fieldset"),
+			h.Label(h.Class("label"), h.Text("Your Nickname"), h.Attr("for", "snake-nickname")),
+			h.Input(
+				h.Class("input input-bordered w-full"),
+				h.ID("snake-nickname"),
+				h.Type("text"),
+				h.Placeholder("Enter your nickname"),
+				nicknameBind,
+				h.Attr("required"),
 			),
 		),
-		h.Div(append([]h.H{h.Class("flex gap-2 justify-center")}, presetButtons...)...),
+	)
+
+	soloSection := h.Div(h.Class("mb-6"),
+		h.H3(h.Class("text-lg font-bold mb-2"), h.Text("Play Solo")),
+		h.Div(append([]h.H{h.Class("flex gap-2 justify-center")}, soloButtons...)...),
+	)
+
+	multiSection := h.Div(h.Class("mb-6"),
+		h.H3(h.Class("text-lg font-bold mb-2"), h.Text("Create Multiplayer Game")),
+		h.Div(append([]h.H{h.Class("flex gap-2 justify-center")}, multiButtons...)...),
 	)
 
 	var gameListEl h.H
@@ -68,7 +92,9 @@ func SnakeLobbyTab(nicknameBind h.H, presetClicks []h.H, activeGames []*snake.Sn
 	}
 
 	return h.Div(
-		createSection,
+		nicknameField,
+		soloSection,
+		multiSection,
 		gameListEl,
 	)
 }