Background Selection state is wrong when SI background is shown

[sangwoo108]

Description

Steps to Reproduce

1. Choose solid/graident background
2. Open new tabs until a new tab has SI background
3. Open background picker on the new tab with SI.

Actual result:

Expected result:

The actual background categroy should be checked.

Reproduces how often:

100%

Brave version (brave://version info)

Version/Channel Information:

• Can you reproduce this issue with the current release?
• Can you reproduce this issue with the beta channel?
• Can you reproduce this issue with the nightly channel?

Other Additional Information:

• Does the issue resolve itself when disabling Brave Shields?
• Does the issue resolve itself when disabling Brave Rewards?
• Is the issue reproducible on the latest version of Chrome?

Miscellaneous Information:

cc @GeetaSarvadnya @kjozwiak

[stephendonner]

Verified PASSED using

Brave	1.45.74 Chromium: 106.0.5249.55 (Official Build) beta (x86_64)
Revision	4d5f098fca6ab7f4b6b7c240be3d9593c2357709-refs/branch-heads/5249@{#531}
OS	macOS Version 11.7 (Build 20G817)

Followed the steps to reproduce, and confirmed Gradients was shown as selected

example	example

[MadhaviSeelam]

Verification PASSED using

Brave | 1.45.75 Chromium: 106.0.5249.65 (Official Build) beta (64-bit)
-- | --
Revision | 3269dc3633cdd2ab94546fdbe54962e45b17a6e0-refs/branch-heads/5249@{#580}
OS | Windows 11 Version 21H2 (Build 22000.978)

Reproduced in 1.44.101 using original STR in the description #25398 (comment)

Steps:

1. Installed 1.45.75
2. launch Brave
3. click Customize
4. selected solid color background
5. opened NTP until a NTPSI background shown
6. click Customize to open Background image setting page

Confirmed Solid colors category that was selected in step 4 remained selected

Also verified for Gradients color category and the selection remained as selected

Solid colors

NTP	NTPSI

Gradients

NTP	NTP SI