Don't start Web Discovery Project in incognito and Tor windows

[remusao]

Resolves brave/brave-browser#18885

Currently the Web Discovery Project is active in Tor and incognito windows (if user opted-in). This is unintended and we do not want WDP running in Tor or incognito windows even after opt-in.

There was a first attempt at fixing this issue here: #10609
But it appears that doing it this way has unintended consequences: launching a Tor window when WDP is enabled will turn it off even for normal windows.

The better fix is to add a check before starting WDP to make sure we are not in an incognito context (which also works for Tor windows).

Submitter Checklist:

• I confirm that no security/privacy review is needed, or that I have requested one
• There is a ticket for my issue
• Used Github auto-closing keywords in the PR description above
• Wrote a good PR/commit description
• Added appropriate labels (QA/Yes or QA/No; release-notes/include or release-notes/exclude; OS/...) to the associated issue
• Checked the PR locally: npm run test -- brave_browser_tests, npm run test -- brave_unit_tests, npm run lint, npm run gn_check, npm run tslint
• Ran git rebase master (if needed)

Reviewer Checklist:

• A security review is not needed, or a link to one is included in the PR description
• New files have MPL-2.0 license header
• Adequate test coverage exists to prevent regressions
• Major classes, functions and non-trivial code blocks are well-commented
• Changes in component dependencies are properly reflected in gn
• Code follows the style guide
• Test plan is specified in PR before merging

After-merge Checklist:

• The associated issue milestone is set to the smallest version that the
  changes has landed on
• All relevant documentation has been updated, for instance:
  • https://github.com/brave/brave-browser/wiki/Deviations-from-Chromium-(features-we-disable-or-remove)
  • https://github.com/brave/brave-browser/wiki/Proxy-redirected-URLs
  • https://github.com/brave/brave-browser/wiki/Fingerprinting-Protections
  • https://github.com/brave/brave-browser/wiki/Brave%E2%80%99s-Use-of-Referral-Codes
  • https://github.com/brave/brave-browser/wiki/Custom-Headers
  • https://github.com/brave/brave-browser/wiki/Web-Compatibility-Exceptions-in-Brave
  • https://github.com/brave/brave-browser/wiki/QA-Guide
  • https://github.com/brave/brave-browser/wiki/P3A

Test Plan:

[iefremov]

i think we need a browser test for this, but can be a follow-up

[kjozwiak]

Verification PASSED on Win 11 running the following build:

Brave | 1.33.33 Chromium: 95.0.4638.54 (Official Build) nightly (64-bit)
-- | --
Revision | d31a821ec901f68d0d34ccdbaea45b4c86ce543e-refs/branch-heads/4638@{#871}
OS | Windows 11 Version 21H2 (Build 22000.258)

Used brave://inspect/#extensions to check WDP.isRunning

• ensured that WDP via brave://settings/search is disabled by default on new profiles
• ensured that WDP.isRunning returns false when WDP is disabled in Normal mode
• ensured that WDP.isRunning returns true when WDP is enabled in Normal mode
• ensured that WDP.isRunning returns undefined via both Tor/Private/Guest when WDP is disabled in Normal mode
• ensured that WDP.isRunning returns undefined via both Tor/Private/Guest windows if already enabled via Normal mode
• ensured that launching a Tor/Private/Guest window doesn't enable or disable WDP via Normal mode

Normal	Tor	Private	Guest