config: Reset per-game profile name on load if empty

src/frontend_common/config.cpp

@@ -138,6 +138,7 @@ void Config::ReadPlayerValues(const std::size_t player_index) {
         if (profile_name.empty()) {
             // Use the global input config
             player = Settings::values.players.GetValue(true)[player_index];
+            player.profile_name = "";
             return;
         }
         player.profile_name = profile_name;

src/yuzu/configuration/qt_config.cpp

@@ -90,6 +90,7 @@ void QtConfig::ReadQtPlayerValues(const std::size_t player_index) {
         if (profile_name.empty()) {
             // Use the global input config
             player = Settings::values.players.GetValue(true)[player_index];
+            player.profile_name = "";
             return;
         }
     }

src/yuzu_cmd/sdl_config.cpp

@@ -103,6 +103,7 @@ void SdlConfig::ReadSdlPlayerValues(const std::size_t player_index) {
         if (profile_name.empty()) {
             // Use the global input config
             player = Settings::values.players.GetValue(true)[player_index];
+            player.profile_name = "";
             return;
         }
     }