[Bug]: "Run Cooked Game" uses Game Cooker's build menu output path instead of last built game's path

### Description

If the game cooker is used via both the preset menu and the build menu, the 'Run Cooked Game' button will use that the build menu's path, even if the last built game was from the preset menu.

It was expected that the 'Run Cooked Game' button would just run whatever game was built last.

On the side, Cook & Run was expected to also use the last utilized build settings as opposed to just using the settings on the build menu.

### Steps to reproduce

1. Build a game using a preset (use an Output path like 'PresetPath/')
2. Build a game using 'Cook & Run' or the standard Build menu in the Game Cooker (use an Output path like 'ClassicBuildPath/').
3. Build a game using the preset again.
4. Delete the game built in the standard build menu (the one at 'ClassicBuildPath/')
5. Click 'Run Cooked Game'

Expected: Flax runs the game built using the preset (the last built game)

Reality: A warning log appears saying `[Warning] Missing executable to run or platform doesn't support build&run.`

### Version

1.12

### Relevant logs

```shell

```

Start by tracing the Game Cooker preset menu, build menu, and the Run Cooked Game action to find where output paths and build settings are stored. Reproduce the sequence using PresetPath/ and ClassicBuildPath/, then verify that Run Cooked Game uses the last built game's path and Cook & Run uses the last-used build settings.

Written by the indexing model from the issue text.