Specified here: https://github.com/brave/brave-core/pull/6949
When Allow Google login for extensions is enabled in extension settings, brave://apps shows sign-in message
Allow Google login for extensions in extension settingsbrave://apps
Comparision Release(back) vs Nightly(middle) vs Beta(front)

No sign-in message irrespective of enabling Google login for extensions
Easy
Brave | 1.14.70 Chromium: 85.0.4183.83聽(Official Build)聽beta聽(64-bit)
-- | --
Revision | 94abc2237ae0c9a4cb5f035431c8adfb94324633-refs/branch-heads/4183@{#1658}
OS | Linux
@brave/legacy_qa to check on other platforms
Does not reproduce on macOS 10.14.6 using any of the following versions:
Release
Brave | 1.13.82 Chromium: 85.0.4183.83聽(Official Build)聽(64-bit)
-- | --
Revision | 94abc2237ae0c9a4cb5f035431c8adfb94324633-refs/branch-heads/4183@{#1658}
OS | macOS Version 10.14.6 (Build 18G3020)
Beta
Brave | 1.14.73 Chromium: 85.0.4183.83聽(Official Build)聽beta聽(64-bit)
-- | --
Revision | 94abc2237ae0c9a4cb5f035431c8adfb94324633-refs/branch-heads/4183@{#1658}
OS | macOS Version 10.14.6 (Build 18G3020)
Dev
Brave | 1.14.72 Chromium: 85.0.4183.83聽(Official Build)聽dev聽(64-bit)
-- | --
Revision | 94abc2237ae0c9a4cb5f035431c8adfb94324633-refs/branch-heads/4183@{#1658}
OS | macOS Version 10.14.6 (Build 18G3020)
Nightly
Brave | 1.15.32 Chromium: 85.0.4183.83聽(Official Build)聽nightly聽(64-bit)
-- | --
Revision | 94abc2237ae0c9a4cb5f035431c8adfb94324633-refs/branch-heads/4183@{#1658}
OS | macOS Version 10.14.6 (Build 18G3020)
Works in Windows 10.
Proof:

Also how did you put label "bug". Some how I can't.
Link:
https://github.com/brave/brave-browser/issues/11586
Updating priority to P3. More info here https://bravesoftware.slack.com/archives/C7VLGSR55/p1603407790308500
Verification passed on
Brave | 1.18.59 Chromium: 87.0.4280.67聽(Official Build)聽dev聽(64-bit)
-- | --
Revision | 0e5d92df40086cf0050c00f87b11da1b14580930-refs/branch-heads/4280@{#1441}
OS | Windows聽10 OS Version 2004 (Build 19041.630)
Reproduced the issue in 1.17.x

Upgraded profile from 1.17.x to 1.18.x and ensured Sign-In with brave does not show up on the top-right corner of the page

Most helpful comment
Does not reproduce on macOS 10.14.6 using any of the following versions:
ReleaseBetaDev
Nightly