NordVPN does not work in Private Mode

[devonandchris]

Description

NordVPN does not work in Private Mode

Steps to Reproduce

1. With a NordVPN account and the NordVPN extension, and the extension enabled for use in private windows, open a private window an attempt to connect to the service.
2. If you have not logged in on a normal tab, you will get prompted to login, and it will appear success, but not actually work.
3. If you have already logged in on a normal tab, you get a pop-up to enter your credentials. Entering your credentials returns you to the request to enter your credentials.

Actual result:

This error is from 0.61.51: Something went wrong: https://i.imgur.com/ezDxIY5.png
VPN credential popup: https://i.imgur.com/gP3ptHA.png

Expected result:

My private window activity is VPNd.

Reproduces how often:

Always happens.

Brave version (brave://version info)

This is present in the current Stable branch:
Version 0.61.52 Chromium: 73.0.3683.86 (Official Build) (64-bit)
This is present in the current Beta branch:
Version 0.63.29 Chromium: 73.0.3683.75 (Official Build) beta (64-bit)
This is present in the current Dev branch:
Version 0.64.30 Chromium: 73.0.3683.75 (Official Build) dev (64-bit)
This is present in the current nightly branch:
Version 0.65.2 Chromium: 73.0.3683.75 (Official Build) nightly (64-bit)

This bug was not always present. Using the mainline branch, it was first noticed with this version:
Version 0.61.51 Chromium: 73.0.3683.75 (Official Build) (64-bit)

Versions prior to this did not exhibit this bug, but I cannot precisely tell you which was the last specific version where this bug did not exist.

I am running OSX Mojave, 10.14.3 (18D109)

I do not have this problem with Chrome incognito windows.

Reproducible on current release:

Yes.

[devonandchris]

Still present in latest update to 0.62.50:

Brave is up to date
Version 0.62.50 Chromium: 73.0.3683.86 (Official Build) (64-bit)