[iOS][autofill] setInputElementValue as util function

This refactoring improves code clarity and simplifies the adoption of
the `gCrWeb` class by isolating internal utility functions and removing
them from the __gCrWeb API.

Bug: 399666983
Change-Id: I4179a184d4519712ebbc29e92eef28f9763708b2
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/7014068
Commit-Queue: Alexandra Pereira <alexandrasp@google.com>
Reviewed-by: Vincent Boisselle <vincb@google.com>
Reviewed-by: Mike Dougherty <michaeldo@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1533775}