Show Brave UA in client side user agent string for DuckDuckGo

[bbraithwaite]

Description

Following on from #10020 would it be possible to extend that functionality to whitelist the useragent further so that it can be accessed via JavaScript e.g. navigator.userAgent on Desktop?

Steps to Reproduce

1. Navigate to duckduckgo.com using Brave (Desktop only)
2. Using the developer console enter navigator.userAgent
3. Expect to see Brave Chome in the user agent string

Actual result:

The string 'Brave' does not appear in the client side user agent.

Expected result:

Show 'Brave Chrome' in the client side user agent string.

Reproduces how often:

Brave Version

about:brave info:

Reproducible on current live release:

Additional Information

[diracdeltas]

It's definitely possible but I'm curious why this is needed

[bbraithwaite]

It's so that we can show promotional content for DDG + Brave in combination. Our SERP has a lot of logic on the front-end by way of JavaScript, therefore being able to know precisely if the user is using the Brave browser allows us to confidently show privacy related features for Brave users.