Change quick search engines settings position

[deeppandya]

Description

Currently we are showing quick search engines option at the end in search engines settings. With this issue, we need to match the position to what we have in IOS.
We need to place quick search engines options right after Standard tab/Private tab.

Steps to reproduce

1. Install Brave
2. Go to settings -> Search engines
3. Observe that Quick search engine option is at the end

Actual result

Expected result

Reproduces how often

Easily reproduced

Brave version

Brave nightly version : 1.75.9

Device

• Brand/model: Pixel 7 pro
• Android version: 15

Channel information

• release (stable)
• beta
• nightly

Reproducibility

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

Miscellaneous information

No response

[kjozwiak]

The above requires 1.74.13 or higher for 1.74.x verification 👍

[hffvld]

Verified on Pixel 7 using version(s):

Device/OS: Pixel 7 / panther_beta-user 15 AP41.240925.009 release-keys
Brave build: 1.74.13 
Chromium: 131.0.6778.85 (Official Build) beta (64-bit) 

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STEPS:

1. Follow the STR/TP from Change quick search engines settings position #42291 (comment)
2. Verify

ACTUAL RESULTS:

• Verified that the Quick-Search Engines settings located between Private Tab and Show browser suggestions settings
• Verified the same for fresh and upgraded profiles.
• Verified that the Quick-Search Engines settings screen can be opened and closed without any issues.

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