[Desktop] [Security] BraveAutocompleteProviderClientForClassifier is leaking OTR profile data

[mkarolin]

Test plan

• Follow steps in Search DuckDuckGo for text in Tor Window still uses Google #1758
• Ensure it still works as expected

Description

This is a follow-up issue for brave/brave-core#5221.
See brave/brave-core#5221 (comment)

When using a Private window, BraveAutocompleteProviderClientForClassifier is likely leaking OTR autocomplete data into the regular profile.

STR: See #1758

cc: @simonhong

[simonhong]

BraveAutocompleteProviderClientForClassifier is introduced to fix #1037. Original PR is brave/brave-core#757. Need to find another way to fix original issue.

[LaurenWags]

Verified passed with

Brave | 1.11.75 Chromium: 83.0.4103.116 (Official Build) dev (64-bit)
-- | --
Revision | 8f0c18b4dca9b6699eb629be0f51810c24fb6428-refs/branch-heads/4103@{#716}
OS | macOS Version 10.14.6 (Build 18G3020)

• Verified STR from Search DuckDuckGo for text in Tor Window still uses Google #1758
• Confirmed using context menu item Search DuckDuckGo for... on a Tor window does use DDG for the search

---

Verification passed on

Brave | 1.11.80 Chromium: 83.0.4103.116 (Official Build) dev (64-bit)
-- | --
Revision | 8f0c18b4dca9b6699eb629be0f51810c24fb6428-refs/branch-heads/4103@{#716}
OS | Windows 10 OS Version 1903 (Build 18362.900)

• Verified STR from Search DuckDuckGo for text in Tor Window still uses Google #1758
• Confirmed using context menu item Search DuckDuckGo for... on a Tor window does use DDG for the search

---

Verified passed with

Brave	1.11.80 Chromium: 83.0.4103.116 (Official Build) dev (64-bit)
Revision	8f0c18b4dca9b6699eb629be0f51810c24fb6428-refs/branch-heads/4103@{#716}
OS	Linux

• Verified STR from Search DuckDuckGo for text in Tor Window still uses Google #1758
• Confirmed using context menu item Search DuckDuckGo for... on a Tor window does use DDG for the search