I did a workaround by editing a script I found and don't understand using xprop, xwininfo, and xdotool. I probably should have mentioned that I'm using X, most of this stuff doesn't work on Wayland. Here's my script so far:

#!/bin/bash

xprop -spy -root _NET_ACTIVE_WINDOW | grep --line-buffered -o '0[xX][a-zA-Z0-9]\{7\}' |
while read -r id; do
    class="`xprop -id $id WM_CLASS 2> /dev/null | grep TeamViewer`"
    if [ -n "$class" ]; then
        if xprop -id "$id" | grep -q 'WM_NAME(STRING) = "TeamViewer Authentication"'; then
            echo "key Tab
            key space
            key shift+Tab
            key shift+Tab
            key Down
            key Tab
            type {my.username}
            key Tab
            key ctrl+u"| xdotool -
            # wait for the window to be closed
            xprop -spy -id $id > /dev/null 2>&1
            fi
    fi
done

It spits out errors after the window closes because I think it's trying to get windows properties from the now closed window, but it gets the job done!

Edit: changed the script to be much smaller and not show errors.