Only seems to affect 0.61.x.
If you navigate to a page like brave://version and then double click in the URL bar (say you want to change version to settings), you'll see that the brave:// part changes to chrome://.
brave:// changes to chrome://

Should stay brave://

easily
Brave | 0.61.41 Chromium: 73.0.3683.39Â (Official Build)Â beta(64-bit)
-- | --
Revision | cc53b0e12fcaf42e4bab8d6c23bd4fb7aae99f6c-refs/branch-heads/3683@{#413}
OS | Mac OS X
Does not reproduce on Dev version 0.62.11

My address bar does not update to chrome, but this may be in the same realm of brave:// urls. Let me know if this should be in its own issue.
I am on 0.60.47, not sure if this is similar enough to be part of this issue but this is what I notice when on brave://about. All the URLS highlighted show chrome at the bottom, but will click through to brave://<item>

Additionally pages such as brave://invalid show a chrome://invalid page.

and the tab shows:

@LaurenWags I think this has been fixed (_"Works for meâ„¢"_), can you confirm?
@bsclifton yep, appears to be working on the following versions:
Brave | 0.69.132 Chromium: 77.0.3865.90Â (Official Build)Â (64-bit)
-- | --
Revision | 58c425ba843df2918d9d4b409331972646c393dd-refs/branch-heads/3865@{#830}
OS | macOS Version 10.13.6 (Build 17G5019)
Brave | 0.70.111 Chromium: 77.0.3865.90 (Official Build) beta (64-bit)
-- | --
Revision | 58c425ba843df2918d9d4b409331972646c393dd-refs/branch-heads/3865@{#830}
OS | macOS Version 10.13.6 (Build 17G5019)
Brave | 0.71.89 Chromium: 77.0.3865.90 (Official Build) dev (64-bit)
-- | --
Revision | 58c425ba843df2918d9d4b409331972646c393dd-refs/branch-heads/3865@{#830}
OS | macOS Version 10.13.6 (Build 17G5019)
Brave | 0.72.83 Chromium: 77.0.3865.90 (Official Build) nightly (64-bit)
-- | --
Revision | 58c425ba843df2918d9d4b409331972646c393dd-refs/branch-heads/3865@{#830}
OS | macOS Version 10.13.6 (Build 17G5019)
Closing this issue.
Most helpful comment
@bsclifton yep, appears to be working on the following versions:
Brave | 0.69.132 Chromium: 77.0.3865.90Â (Official Build)Â (64-bit)
-- | --
Revision | 58c425ba843df2918d9d4b409331972646c393dd-refs/branch-heads/3865@{#830}
OS | macOS Version 10.13.6 (Build 17G5019)
Brave | 0.70.111 Chromium: 77.0.3865.90 (Official Build) beta (64-bit)
-- | --
Revision | 58c425ba843df2918d9d4b409331972646c393dd-refs/branch-heads/3865@{#830}
OS | macOS Version 10.13.6 (Build 17G5019)
Brave | 0.71.89 Chromium: 77.0.3865.90 (Official Build) dev (64-bit)
-- | --
Revision | 58c425ba843df2918d9d4b409331972646c393dd-refs/branch-heads/3865@{#830}
OS | macOS Version 10.13.6 (Build 17G5019)
Brave | 0.72.83 Chromium: 77.0.3865.90 (Official Build) nightly (64-bit)
-- | --
Revision | 58c425ba843df2918d9d4b409331972646c393dd-refs/branch-heads/3865@{#830}
OS | macOS Version 10.13.6 (Build 17G5019)
Closing this issue.