Top sites are not re-added once all the top sites are removed

[GeetaSarvadnya]

Description

Top sites are not re-added once all the top sites are removed

Steps to Reproduce

1. Clean profile 1.17.53
2. Visit 4 to 5 sites
3. Make sure top sites are added in NTP's
4. Remove all the top sites one by one by clicking on the X icon
5. Make sure all the top sites are removed
6. Re-visit all the sites opened in step 2 (I have visited all the sites min 10 times)
7. Open an NTP observe no top sites are added
8. Restart the browser and re-visit all the sites again, no top sites are re-added in NTP's

Note: Follow the same steps in 1.16.68 works fine, top sites are re-added.

Actual result:

Top sites are not re-added once all the top sites are removed

Expected result:

Top sites should be re-added

Reproduces how often:

Always

Brave version (brave://version info)

Brave	1.17.53 Chromium: 86.0.4240.111 (Official Build) dev (64-bit)
Revision	b8c36128a06ebad76af51591bfec980224db5522-refs/branch-heads/4240@{#1290}
OS	Windows 10 OS Version 1903 (Build 18362.1139)

Version/Channel Information:

• Can you reproduce this issue with the current release? No
• Can you reproduce this issue with the beta channel? Yes
• Can you reproduce this issue with the nightly channel? Yes

Other Additional Information:

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

Miscellaneous Information:

cc: @brave/legacy_qa @bsclifton @rebron

[kjozwiak]

This might not be 100% fixed as per #12739. Waiting on some info from @simonhong.

[LaurenWags]

Verified passed with

Brave | 1.17.70 Chromium: 87.0.4280.60 (Official Build) (x86_64)
-- | --
Revision | 12697cfeb273d7de95cf9b18350d2c457f58224c-refs/branch-heads/4280@{#1352}
OS | macOS Version 10.14.6 (Build 18G6042)

Verified test plan from brave/brave-core#7105

Confirmed the Customize Top Sites toggle under the Customization modal as been removed:

Confirmed that use_most_visited_tiles is set as true under brave://prefs-internals:

STR still reproduced for me, but this was mentioned by @kjozwiak in #12378 (comment) and is covered by #12739

---

Verification passed on

Brave	1.17.70 Chromium: 87.0.4280.60 (Official Build) (64-bit)
Revision	12697cfeb273d7de95cf9b18350d2c457f58224c-refs/branch-heads/4280@{#1352}
OS	Windows 7 Service Pack 1 (Build 7601.24544)

The issue still reproduces and is covered by #12739