Identity internals: Remove use of deprecated cr/ui.m.js

This is in preparation for migrating to TypeScript.

Bug: 1316438
Change-Id: I049a67642d9b81707a1da906926b3d1c06aa583e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3626353


Reviewed-by: Demetrios Papadopoulos <dpapad@chromium.org>
Commit-Queue: Rebekah Potter <rbpotter@chromium.org>
Cr-Commit-Position: refs/heads/main@{#999984}