Reland [E2E] Set the right navigation bar color when going from E2E to non E2E

Before: https://hsv.googleplex.com/5445338855899136
After: https://hsv.googleplex.com/5793187317678080

Verification steps:
1. Enable E2e flags (#draw-cutout-edge-to-edge and #draw-edge-to-edge)
2. Make sure you're in light theme
3. Go to a page that doesn't support E2E (ex: Wikipedia). The navigation bar should be white in light theme.
4. Go to a page that supports E2E (ex: Apple.com)
5. Navigate back to Wikipedia (I used back gesture in gesture navigation mode). Before: navigation bar shows up black. After: navigation bar shows up as the right color.

Fixed: b/41485486
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5346729


Reviewed-by: Lijin Shen <lazzzis@google.com>
Reviewed-by: Theresa Sullivan <twellington@chromium.org>
Commit-Queue: Geoff Huang <geoffhuang@google.com>
Cr-Original-Commit-Position: refs/heads/main@{#1269298}
Change-Id: I62291bee3aef244421c3845ebc337a6cd2971989
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5354152
Cr-Commit-Position: refs/heads/main@{#1270573}