Launching any cli app(such as powershell, wsl) sets the tab's icon as the default profile's icon

[rounk-ctrl]

Windows Terminal version (or Windows build number)

10.0.22000.65, 1.10.1933.0

Other Software

No response

Steps to reproduce

Set default terminal application as windows terminal preview.
Use search to open powershell(or wsl)
See tab icon as the default profile's icon

Expected Behavior

See the tab's icon as the app's icon.

Actual Behavior

The tab's icon is the default profile's icon.

[zadjii-msft]

You know, I could have sworn we had an issue tracking this, but looking at https://github.com/microsoft/terminal/issues?q=is%3Aopen+is%3Aissue+label%3AArea-DefApp, looks like we don't.

I believe the plan of record is to use the settings in profiles.defaults for connections spawned via the defterm connection.

[zadjii-msft]

Maintainer note: When we get around to doing this, we should simultaneously do #6776, with a similar style fix.