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.