Can I target a given Windows Terminal "session" when invoking `wt.exe`?
It sounds like you are looking for the (at the time of this answer) relatively new -w argument to specify a window-name. E.g.:
wt.exe -w 0 -p "Git Bash" ...
The current window is always "0", but you can name them whatever you want. If you want to guarantee a single Windows Terminal window, however, stick to "0".
Here is the Microsoft doc for more information.