Reload new incognito tab resets DDG search button

[srirambv]

Description

Reload new incognito tab resets DDG search button

Steps to Reproduce

1. Clean install 0.55.5
2. Open an incognito window
3. Toggle DDG search, reload the new tab page, switch toggles back to off
4. Do a search on DDG in incognito tab
5. Open a new tab in incognito window, DDG is set as default search, reload new tab doesn't toggle the switch

Actual result:

This is the same behaviour on all platforms until a search is done on DDG

On Windows 10 DDG search fails making it impossible to use DDG and reload always resets the switch

Expected result:

Once switch is enabled should be retained after page is reloaded

Reproduces how often:

Easy

Brave version (chrome://version info)

Brave	0.55.2 Chromium: 70.0.3538.16 (Official Build) (64-bit)
Revision	16ed95b41bb05e565b11fb66ac33c660b721f778-refs/branch-heads/3538@{#306}
OS	All

Reproducible on current release:

N/A

Website problems only:

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

Additional Information

It also works the other way. Have DDG persist, open new private tab, turn DDG off and reload.
issue verified by @LaurenWags @kjozwiak on mac and @btlechowski on Windows 7

[srirambv]

Verification Passed on

Brave	0.55.11 Chromium: 70.0.3538.35 (Official Build) beta (64-bit)
Revision	28dcb499844fa40c28d5f62e337876cb936f79f5-refs/branch-heads/3538@{#678}
OS	Linux

• Verified enabling DDG switch and reloading page didn't reset the setting
• Verified after enabling DDG button typing a search term showed DuckDuckGo Search
• Verified after disabling DDG button typing a search term showed Google Search
• Verified enabling DDG button is retained across private browsing session
• Verified enabling DDG button is retained across private tabs

Verified passed with

Brave	0.55.11 Chromium: 70.0.3538.35 (Official Build) beta(64-bit)
Revision	28dcb499844fa40c28d5f62e337876cb936f79f5-refs/branch-heads/3538@{#678}
OS	Mac OS X

• Verified enabling DDG switch and reloading page didn't reset the setting
• Verified after enabling DDG button typing a search term showed DuckDuckGo Search
• Verified after disabling DDG button typing a search term showed Google Search
• Verified enabling DDG button is retained across private browsing session
• Verified enabling DDG button is retained across private tabs

Verification passed on

Brave	0.55.11 Chromium: 70.0.3538.35 (Official Build) beta (64-bit)
Revision	28dcb499844fa40c28d5f62e337876cb936f79f5-refs/branch-heads/3538@{#678}
OS	Windows 7

• Verified enabling DDG switch and reloading page didn't reset the setting
• Verified after enabling DDG button typing a search term showed DuckDuckGo Search
• Verified after disabling DDG button typing a search term showed Google Search
• Verified enabling DDG button is retained across private browsing session
• Verified enabling DDG button is retained across private tabs