Change the delay that occurs after entering an incorrect password in the gdm3 login-screen?

After a lot of digging into the gnome-shell and gdm source code, the problem seems to have been fixed by these two commits:

• f4d90bc127ececb653ee399493839f17932b7622 - "polkitAgent: Reset the session request timeout when removing it"

• 8d139bbd95a5d62e0ba20b711a10a8b669cb9e9d - "authPrompt: Grab key focus when making entry sensitive"

These fix the issue where the input box doesn't get focused for 3 seconds after the shaking stops.

These changes are there in Gnome 3.36.2, and updating to that version fixes the issue. Now you can type even while the box is shaking.

To disable the shaking see @PRATAP's answer.

Workaround based on the update in the Question

An Idea of mine was maybe disable the shaking animation will help? Because I found out, that you can use the mouse to click into the field and you can type immediately while the box is shaking.

Shacking animation can be disabled if you wish to stop the global animation by running the below command for the desktop session..

gsettings set org.gnome.desktop.interface enable-animations false

The above command helps for the lock screen..

If you wish to disable the shacking animation for the login screen too.. run the below command..

sudo -Hu gdm dbus-launch gsettings set org.gnome.desktop.interface enable-animations false

for reverting above changes..

gsettings set org.gnome.desktop.interface enable-animations true

and

sudo -Hu gdm dbus-launch gsettings set org.gnome.desktop.interface enable-animations true

Tested in Ubuntu 20.04 for both lock and login screens..