Paste is annoyingly asynchronous wrt typeahead

### Windows Terminal version

1.17.1023

### Windows build number

10.0.19045.2846

### Other Software

git version 2.40.0.windows.1

### Steps to reproduce

Run Git Bash in Windows Terminal, while other processes are causing CPU and paging load.

Copy some text to the Clipboard from another application. (For example, copy a Git commit ID.)

In Git Bash, type some characters, press Shift+Insert to paste, and type more characters. (For example, type `git cherry-pick ` initially, and press Enter at the end.)

### Expected Behavior

Pasted text should appear in the correct place between the first and second sequence of characters.

### Actual Behavior

Pasted text occasionally appears after the second sequence of characters. As if Shift+Insert starts an asynchronous paste operation that completes at some later time and injects its result into the terminal input at that time.

Start by reproducing the race in Git Bash under CPU and paging load on Windows Terminal 1.17.1023, using Shift+Insert between two typed sequences. Trace the paste and terminal input handling to determine why pasted text is inserted asynchronously; done means the pasted text consistently appears between the two sequences.

Written by the indexing model from the issue text.