Update FieldDataManager earlier about text-changes

On text field changes the following occurs:
1) Autofill receives a notification about the change.
2) Autofill informs FormTracker about the change.
3) FormTracker receives the signal, does some async posting and
   ultimately updates submission data (which includes a form
   extraction A).
4) FormTracker sends the signal back to AutofillAgent.
5) AutofillAgent updates the FieldDataManager with the given change.
6) AutofillAgent informs PasswordAutofillAgent of the change.
7) PasswordAutofillAgent processes this (which includes a form
   extraction B) and informs the browser about this.

Step 5 updates the data required to compute
FormFieldData::properties_mask_ and FormFieldData::user_input_, which
means that extraction A that happened in Step 3 contained wrong
information, whereas the one that happened in B didn't.

This becomes problematic with the AutofillOptimizeFormExtraction
experiment because we want to extract once and reuse everywhere. This
CL therefore moves the current Step 5 to start happening in between
current Steps 1 and 2.

Bug: 40947729
Change-Id: Ibe846006bc496e28c1043a2ef27c169b287de65b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6170228
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Reviewed-by: Christoph Schwering <schwering@google.com>
Reviewed-by: Maria Kazinova <kazinova@google.com>
Commit-Queue: Jihad Hanna <jihadghanna@google.com>
Cr-Commit-Position: refs/heads/main@{#1407882}