gaming: pin Steam Big Picture + games to DP-1/ws3

Big Picture shares the plain `steam` WM_CLASS, so it opened on whatever
monitor the cursor was on rather than the streamed one; match its title
instead and pin to ws3 (DP-1's persistent workspace, what the stream
captures). Move the steam_app_ game rule from ws6 to ws3 too so games and
Big Picture share one streamed workspace and launching a game doesn't flip
DP-1 to a different workspace.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

home/konishi/default.nix

@@ -62,13 +62,22 @@
       "move 100%-w-20 100%-h-20, match:title egui-.*"
 
       # gaming: Steam/Proton titles run under XWayland with WM_CLASS
-      # steam_app_<appid>. Send them fullscreen to workspace 6 (DP-1, top-left)
-      # instead of opening tiled on whatever monitor Steam is on.
+      # steam_app_<appid>. Send them fullscreen to workspace 3 (DP-1) — the same
+      # streamed workspace as Big Picture below — instead of opening tiled on
+      # whatever monitor Steam is on.
       # Native (non-Proton) games have their own class — grab it with
       # `hyprctl clients | grep -iE "class|title"` while the game runs and add a
       # matching line here.
-      "workspace 6, match:class steam_app_.*"
+      "workspace 3, match:class steam_app_.*"
       "fullscreen on, match:class steam_app_.*"
+
+      # Steam Big Picture shares the plain `steam` WM_CLASS with the normal
+      # client, so match its title instead. Without this it opens on whatever
+      # monitor the cursor is on, not the streamed one. Pin it to ws3 — DP-1's
+      # normal persistent workspace, which is what the stream captures. `.`
+      # stands in for the literal spaces to keep the rule string unambiguous.
+      "workspace 3, match:title Steam.Big.Picture.Mode"
+      "fullscreen on, match:title Steam.Big.Picture.Mode"
     ];
 
     render = {