Different behavior of loading brave://settings and chrome://settings in private window

[simonhong]

Description

When typing brave://settings and chrome://settings in private window's omnibox,
both shows different result.
brave://settings is opened in private window and chrome://settings is opened in normal window.

Steps to Reproduce

1. Typing brave://settings and chrome://settings in private window's omnibox
2. Check the opened window (private or normal window)

Actual result:

Both are opened in different window.
brave://settings is opened in private window.
chrome://settings is opened in normal window.

Expected result:

Both should be opened in normal window.

Reproduces how often:

Always.

Brave version (brave://version info)

All current channels.

Reproducible on current release:

• Does it reproduce on brave-browser dev/beta builds?
  Yes

Website problems only:

• Does the issue resolve itself when disabling Brave Shields? No
• Is the issue reproducible on the latest version of Chrome? No

Additional Information

Mapping from brave to chrome is not applied when page is checked whether allowed in private window or not.

[btlechowski]

Verification passed on

Brave	0.62.10 Chromium: 73.0.3683.39 (Official Build) dev (64-bit)
Revision	cc53b0e12fcaf42e4bab8d6c23bd4fb7aae99f6c-refs/branch-heads/3683@{#413}
OS	Windows 7 Service Pack 1 Build 7601.24312

brave://settings and chrome://settings are opened in normal window.

Encountered #2995 while testing.

Verification passed on

Brave	0.62.26 Chromium: 73.0.3683.75 (Official Build) beta (64-bit)
Revision	909ee014fcea6828f9a610e6716145bc0b3ebf4a-refs/branch-heads/3683@{#803}
OS	Linux

• Verified the STR mentioned in the description
• Encountered [Desktop] Remove Sync from brave://settings under Tor/Guest Windows #2995

Verified passed with

Brave	0.62.28 Chromium: 73.0.3683.75 (Official Build) beta(64-bit)
Revision	909ee014fcea6828f9a610e6716145bc0b3ebf4a-refs/branch-heads/3683@{#803}
OS	Mac OS X

• Verified with STR from description