Split enter password function.

I temporarily left the old behavior to not break the test.
The reason of the split, it seems the tast test is failing because the button is not enabled when the click happens, also with this split makes the debugging easier I think.

Bug: b:329361749
Change-Id: Ia7205c17251befa346f4a5fa5378506802215ff4
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5380466
Reviewed-by: Bohdan Tyshchenko <bohdanty@google.com>
Commit-Queue: Istvan Nagy <iscsi@google.com>
Cr-Commit-Position: refs/heads/main@{#1276308}