Turn Improve Search suggestions setting to default on for Brave Search

[rebron]

Description

• The Improve Search suggestions setting (previously named Autocomplete searches and URLs) should be defaulted on for the following regions for IN / CA / DE / FR / GB / US / AT / ES / MX / BR / AR for new and existing Brave Search users.
• Move Improve search suggestions option to brave://settings/search #30878

Design (placeholder)

Brave version (brave://version info)

Target version tbd.

Version/Channel Information:

• Can you reproduce this issue with the current release? n/a
• Can you reproduce this issue with the beta channel? n/a
• Can you reproduce this issue with the nightly channel? n/a

Other Additional Information:

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

Miscellaneous Information:

Related: #18331, #23814, #26181, #27709

[rebron]

cc: @aguscruiz design mock of setting in the proper location when you get a chance, should be a quick one.

[simonhong]

should be defaulted on for the following regions for IN / CA / DE / FR / GB / US / AT / ES / MX / BR / AR for new and existing Brave Search users.

@rebron When we set on as a default for these regions and Brave Search users,
then we should set off again when users in that area choose another search provider?

[rebron]

@simonhong Yes. Should act similarly to how we do autocomplete suggestions. It maybe that we need to change the UI/UX for this and make it a checkbox.

[simonhong]

Ok, got it. changing default value based on current search provider.
Whenever user change search provider, set default value as On if user selected Brave Search.
Otherwise, set default value Off.

and IMO current toggle box seems ok because we only need to control its on/off?

[aguscruiz]

Here's the design for the prompt we can use on the omnibar.
https://www.figma.com/file/tLXWGCpNoiJxDZDdpfordj/Desktop-Settings?type=design&node-id=4140%3A76920&mode=design&t=2Rffs9nWS7DEnyrJ-1