Default search should be versioned

[bsclifton]

Test plan

See brave/brave-core#7090

Description

Right now, there's not a way to tell what the default search engine was when the user's profile was created.
If the default is changed, anyone who has not set the search engine explicitly will get the NEW default.

Steps to Reproduce

1. Fresh profile
2. Take note of the default search engine Brave uses when searching on regular window/tabs (ex: Google)
3. Have a developer update the code to change the default for that region (ex: Bing)

Actual result:

It doesn't matter if person had been using the default. The new default will be used instead (ex: Bing). The only way the value is retained is when they have changed the default explicitly

Expected result:

If user profile has existed for a while, the original provider for default search engine should be preserved (ex: Google in this case)

Reproduces how often:

100%

[LaurenWags]

Desktop can be tested via test plan in brave/brave-core#7090, however pending Android specific test plan from @bsclifton 👍

[btlechowski]

Verification passed on

Brave	1.18.69 Chromium: 87.0.4280.88 (Official Build) (64-bit)
Revision	89e2380a3e36c3464b5dd1302349b1382549290d-refs/branch-heads/4280@{#1761}
OS	Windows 7 Service Pack 1 (Build 7601.24544)

Verified test plan from brave/brave-core#7090 (some verification were done in #12327)

Verified Russia on upgraded profile from 1.17.x
On 1.17.x google is default

On 1.18.x google is default, but Yandex has been added to suggested list

---

Verification passed on LG Nexus 5 with Android 5.1 running 1.18.70 Bravearm.apk

Verified test plan from brave/brave-core#7090 (comment) for Armenian and Russian.

For a new profile, confirmed that Yandex was selected as the default search engine for Armenian and Russian (Uzbek not available on device). Confirmed Yandex is default in Settings and selected by default on Onboarding.

For existing profile with default SE never modified, confirmed that updating from 1.17.75 CR: 87.0.4280.88 --> 1.18.70 Chromium: 87.0.4280.101 didn't replace the previous default SE of Google with Yandex. Tested for both Armenian and Russian.

For existing profile with default SE changed, confirmed that updating from 1.17.75 CR: 87.0.4280.88 --> 1.18.70 Chromium: 87.0.4280.101 didn't replace the previous selected SE of DDG with Yandex. Tested for both Armenian and Russian.

Note: Some of these regions don't have any localization but I ensured that:

• Yandex is being set as the default
• Yandex is available via the SE onboarding

Armenian new profile

Onboarding	Settings

Russian new profile

Onboarding	Settings

Additional testing notes can be found under #12979 (comment)