brave://settings/content page settings are not shown until the page is refreshed

[GeetaSarvadnya]

Description

Found while testing #35369
brave://settings/content page settings are not shown until the page is refreshed

Steps to Reproduce

1. Clea profile 1.62.149
2. Open brave://settings/privacy
3. Click on Site and Shield Settings
4. Content settings are NOT shown
5. Reload the page
6. Content settings are shown

Actual result:

brave://settings/content page settings are not shown until the page is refreshed

Expected result:

Content settings should be shown when user click on the Site and Shield Settings without page refresh

Reproduces how often:

Easy

Brave version (brave://version info)

Brave	1.62.149 Chromium: 121.0.6167.75 (Official Build) (64-bit)
Revision	ff84587bd70af9fcbcbe59fc5194ca65082759c4
OS	Windows 10 Version 22H2 (Build 19045.3930)

Version/Channel Information:

• Can you reproduce this issue with the current release? No
• Can you reproduce this issue with the beta channel? No
• Can you reproduce this issue with the nightly channel? Yes in 1.64.5 Chromium: 121.0.6167.75

Other Additional Information:

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

Miscellaneous Information:

cc: @rebron @mkarolin @brave/qa-team

[GeetaSarvadnya]

Looks like the issue got introduced during the minor bump as the issue was not reproducible in the version 1.64.2 Chromium: 121.0.6167.57 on nightly but it got introduced in the version 1.64.5 Chromium: 121.0.6167.75

[kjozwiak]

The above requires 1.62.50 for 1.62.x verification 👍

[GeetaSarvadnya]

Verification PASSED on

Brave | 1.62.150 Chromium: 121.0.6167.85 (Official Build) (64-bit)
-- | --
Revision | c01f5cde4d5d5e41134c0ccdb1868acd80a64a34
OS | Windows 10 Version 22H2 (Build 19045.3930)

Confirmed that the click on Site and Shield Settings opens up the brave://settings/content page and settings are shown as expected.