Cleanup html/css for NTP Customize Chrome buttons

The html and css for Customize Chrome buttons was getting too messy.
Nothing should change visually with these changes, other than actually
using our non-hover background color and removed forced colors for high
contrast mode. It is mostly code cleanup.

Changes of note:
* All checks for GM3 were removed since GM3 is default on now. This
  includes everything in this file, not just the buttons. However,
  almost all of it was in the buttons.
* Removed the movement left part of the animation on the wallpaper
  search button. I don't notice a visual difference, and it was
  causing the button to not be where it is supposed to be. I'm not
  sure how it was working before.
* We actually were using our hover color as our color for the buttons.
  I assume that was a bug because it didn't make sense to set the
  non-hover color and immediately override it with the hover color.
  Ignoring whether it is currently being hovered on or not.
* Switched to using cr-icon.
* Removed the button containers. There was a comment claiming that the
  containers have to be there because cr-button has a transparent
  background. However, we can override the background color for a
  cr-button, so that is unnecessary.
* Removed all styles related to forced-colors. cr-button has styles for
  that (though I think they just turn it off). We shouldn't need to
  write our own styles here.

Lots of screenshots:
Both buttons:
CWS theme: http://screenshot/BRnuZM5fm3ScdNT
Wallpaper Search open: http://screenshot/3w5mfsRnAQtxHt5
Light mode default GM3: http://screenshot/5avU39BoDrJmWZL
Dark mode default GM3: http://screenshot/8pinYpopFJX6sgW
Light mode GM3: http://screenshot/3TEjp8zqTgAtaqD
Dark mode GM3: http://screenshot/67xnnzDxTSnWEHo
Background image: http://screenshot/BQXJC7F9jsL7Nyt

Just Customize chrome button:
CWS theme: http://screenshot/45DoKW6ot2bhXKx
Light mode default GM3: http://screenshot/4okoXAyc2PWvtvo
Dark mode default GM3: http://screenshot/7sNroB7LUNnvxgP
Light mode GM3: http://screenshot/BWjUetQRC7ws7D6
Dark mode GM3: http://screenshot/GcnRfTUpCmxJzFX
Background image: http://screenshot/4xisSEVcoGNJAHC

Animation video:
http://screencast/cast/NTc1NTUwNDgwMTM0OTYzMnxlY2M2MTExYS1jZQ

Bug: 331689355
Change-Id: Ie988530d28dbaed3ea9506478e9eb9e157cbc83e
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5401468


Reviewed-by: John Lee <johntlee@chromium.org>
Commit-Queue: Riley Tatum <rtatum@google.com>
Reviewed-by: Paul Adedeji <pauladedeji@google.com>
Cr-Commit-Position: refs/heads/main@{#1280277}