Search Engine of address bar in Private Window is wrongly using the Default Search Engine

[skyz91]

Description

The private window address bar in using the wrong search engine. It should use the one I select in the Settings.

Steps to reproduce

1. Select a default Search Engine and a different Search Engine in Private Mode
2. Perform a Search in the address bar in Private mode.
3. Search is processed by the Default Search Engine.

Actual result

Private.Search.Engine.Problem.mp4

Expected result

The correct Search Engine of Private Mode should be used.

Reproduces how often

Easily reproduced

Brave version (brave://version info)

1.73.104 Chromium: 131.0.6778.204 (Official Build) (64-bit)

Channel information

• release (stable)
• beta
• nightly

Reproducibility

• with Brave Shields disabled
• with Brave Rewards disabled
• in the latest version of Chrome

Miscellaneous information

I noticed a similar problem that was brought up (see Issue #42989) but it was for Nightly and it was about the Search of text with the context menu, so I opted to open a new Issue. However, they very well may be related.

[issuant]

This happens occasionally on Android too.