Developer mode extensions warning is shown after restart

[btlechowski]

Follow up to: #4349

Steps to Reproduce

1. Open https://developer.chrome.com/extensions/samples in a new tab
2. Download one of the sample extensions and unzip
3. Visit chrome://extensions/
4. Enable developer mode
5. Click Load unpacked and then pick the folder where the extension was unzippped (step 2)
6. Restart browser
7. Wait 15 seconds

Actual result:

Warning is shown on startup

Expected result:

Warning should not be shown on startup

Reproduces how often:

Easily reproduced

Brave version (brave://version info)

Brave	0.68.128 Chromium: 76.0.3809.100 (Official Build) beta (64-bit)
Revision	ed9d447d30203dc5069e540f05079e493fc1c132-refs/branch-heads/3809@{#990}
OS	Windows 7 Service Pack 1 (Build 7601.24494)

Related issues: #5063

cc @brave/legacy_qa @bsclifton

[btlechowski]

Not reproducible on Ubuntu

Brave	0.68.128 Chromium: 76.0.3809.100 (Official Build) beta (64-bit)
Revision	ed9d447d30203dc5069e540f05079e493fc1c132-refs/branch-heads/3809@{#990}
OS	Ubuntu 18.04 LTS

[rebron]

cc: @tomlowenthal We do want this notification shown in release channel right?

[tildelowengrimm]

@rebron Yes, this looks like the correct behavior to me.