Starting Windows Terminal with Win+X should lead to a different default profile

### Windows Terminal version

1.13.11432.0

### Windows build number

10.0.22000.708

### Other Software

_No response_

### Steps to reproduce

1. Setup WSL as your default profile in windows terminal (or azure...)
2. Press Win+X then I or A to start the windows terminal in normal or administrative mode
3. This will open the default profile which can be WSL2 if you use Linux a lot, while you would not expect a linux profile from a default Win+X keyboard sequence

### Expected Behavior

Win+X then I or A should start a Windows native prompt, as people starting Windows Terminal with the Win+X sequence are more likely to need PowerShell (or the command prompt) than Linux or Azure etc.

Consequently, there should be at least 3, more likely 4 different "default" profiles corresponding to the different context in which WT can be started:
- the regular default profile for when WT is started from the start menu or the taskbar (regular use): whatever the user has currently setup as a default
- the WinX default profile for when WT is started from the key sequence Win+X: typically for maintenance, like by following step-by-step instruction guides
- the QuakeMode default profile for when WT is started from Alt+`: typically to quickly run commands as an overlay (therefore without tabs, titlebars etc)
- (the 4th one would separate Win+X I and Win+X A)

Making these defaults configurable could allow say sticking to the command prompt for one of the Win+X sequences while preferring PowerShell for the other.

This means a typical user could start WT in 4 different ways:
- click on the icon to start WSL2
- press Win+X I to start a normal command prompt
- press Win+X A to start an elevated PowerShell
- press Alt-` to start git bash

### Actual Behavior

Win+X then I or A starts the default profile, with no further distinction.

Likewise, Alt+` brings the current WT windows with any tab currently opened

Start by reproducing launches from Win+X I, Win+X A, the regular app entry, and Quake Mode with a non-native default profile. Trace how each launch selects the profile, then define configurable defaults for the requested contexts and verify that each shortcut opens the intended profile without changing the regular default.

Written by the indexing model from the issue text.