Restore open search behaviour for Android

[samartnik]

Description

Recent PR brave/brave-core#9602 caused a regression in Android behavour, we need to restore it until we figure out what we want to do with this option.

Steps to reproduce

1. On Android, visit a search engine and perform a search (user used searx.be)
2. After performing the search, check Settings --> Search engines --> Recently visited and observe no searches have been added

Actual result

No recently visited search engines.

Expected result

There should be recently visited search engines.

Issue reproduces how often

Version/Channel Information:

• Can you reproduce this issue with the current Play Store version?
• Can you reproduce this issue with the current Play Store Beta version?
• Can you reproduce this issue with the current Play Store Nightly version?

Device details

• Install type (ARM, x86):
• Device type (Phone, Tablet, Phablet):
• Android version:

Brave version

Website problems only

• Does the issue resolve itself when disabling Brave Shields?
• Does the issue resolve itself when disabling Brave Rewards?
• Is the issue reproducible on the latest version of Chrome?

Additional information

[srirambv]

Verification passed on the following devices running 1.33.114 x64 build

• Verified steps from issue description
• Verified performing a search on a page that supports open search gets listed under Recently visited
• Verified able to select the search engine added via open search and set it as default
• Verified open search engine gets listed for both normal and private search engine settings
• Verified able to switch back to default list which moves the added search engine back to recently visited list

Oppo Reno 5 (Android 11)	Samsung Tab A (Android 10)
Open.Search.Android.ARM.mp4	Open.Search.Android.Tab.mp4