In the windows terminal, can I start ubuntu from current directory while keep it starting from /home/$user/ if clicking the app directly?

I use the Windows subsystem for Linux ubuntu distribution in the Windows Terminal.

First I want to start the terminal from the current directory that I open in the file explorer. Therefore, I set "startingDirectory": "." in the settings.json following this answer. Then if I type wt in the address bar, Windows Terminal pops out and starts from the current folder, which is what I desire.

Next, I still want to keep the terminal opening from the ~ home directory when I directly open the app from start menu.

Is it possible to manage both things here? Thanks!