Merge pull request #2016 from brave/sync_dont_send_bookmarks_when_no_…

[AlexeyBarabash]

…chain

This is uplift request of #2016 into 0.63.x

Fixes brave/brave-browser#3777 (Sync: not all bookmarks synced).
Fixes brave/brave-browser#3509 (Bookmarks are synced when not connected to sync chain).
Fixes brave/brave-browser#2687 (Sync sends bookmarks even when chain is not fully created).

For #3509 and #2687 fix is obvious.
For #3777 description is brave/brave-browser#3777 (comment).

Submitter Checklist:

• Submitted a ticket for my issue if one did not already exist.
• Used Github auto-closing keywords in the commit message.
• Added/updated tests for this change (for new code or code which already has tests).
• Verified that these changes build without errors on
  • Windows
  • macOS
  • Linux
• Verified that these changes pass automated tests (npm test brave_unit_tests && npm test brave_browser_tests) on
  • Windows
  • macOS
  • Linux
• Verified that all lint errors/warnings are resolved (npm run lint)
• Ran git rebase master (if needed).
• Ran git rebase -i to squash commits (if needed).
• Tagged reviewers and labelled the pull request as needed.
• Request a security/privacy review as needed.
• Add appropriate QA labels (QA/Yes or QA/No) to include the closed issue in milestone

Test Plan:

Use STR from
brave/brave-browser#3777
brave/brave-browser#3509
brave/brave-browser#2687

Reviewer Checklist:

• New files have MPL-2.0 license header.
• Request a security/privacy review as needed.
• Adequate test coverage exists to prevent regressions
• Verify test plan is specified in PR before merging to source

[rebron]

Looks good.

[AlexeyBarabash]

Checked, it works on nightly build.