Poll device list during long initial commits procedure

[AlexeyBarabash]

Issue happens because at Syncer::BuildAndPostCommits loop is executed till all the records will be sent. It can take significant amount of time, ~10 minutes for 20k records, and during this time device can't receive updates.

This PR adds forced get updates only of device type to get the updates if large commit initial happens.

Resolves brave/brave-browser#27931

Submitter Checklist:

• I confirm that no security/privacy review is needed, or that I have requested one
• There is a ticket for my issue
• Used Github auto-closing keywords in the PR description above
• Wrote a good PR/commit description
• Squashed any review feedback or "fixup" commits before merge, so that history is a record of what happened in the repo, not your PR
• Added appropriate labels (QA/Yes or QA/No; release-notes/include or release-notes/exclude; OS/...) to the associated issue
• Checked the PR locally:
  • npm run test -- brave_browser_tests, npm run test -- brave_unit_tests wiki
  • npm run lint, npm run presubmit wiki, npm run gn_check, npm run tslint
• Ran git rebase master (if needed)

Reviewer Checklist:

• A security review is not needed, or a link to one is included in the PR description
• New files have MPL-2.0 license header
• Adequate test coverage exists to prevent regressions
• Major classes, functions and non-trivial code blocks are well-commented
• Changes in component dependencies are properly reflected in gn
• Code follows the style guide
• Test plan is specified in PR before merging

After-merge Checklist:

• The associated issue milestone is set to the smallest version that the
  changes has landed on
• All relevant documentation has been updated, for instance:
  • https://github.com/brave/brave-browser/wiki/Deviations-from-Chromium-(features-we-disable-or-remove)
  • https://github.com/brave/brave-browser/wiki/Proxy-redirected-URLs
  • https://github.com/brave/brave-browser/wiki/Fingerprinting-Protections
  • https://github.com/brave/brave-browser/wiki/Brave%E2%80%99s-Use-of-Referral-Codes
  • https://github.com/brave/brave-browser/wiki/Custom-Headers
  • https://github.com/brave/brave-browser/wiki/Web-Compatibility-Exceptions-in-Brave
  • https://github.com/brave/brave-browser/wiki/QA-Guide
  • https://github.com/brave/brave-browser/wiki/P3A

Test Plan:

import_20k.zip

Test plan

1. For device1 import bookmarks from import_20k/import1 folder from attached zip. Similar for device2 => import_20k/import1;
2. On device1 create the sync chain;
3. Connect device2 to the sync chain, expected ti see device1 in devices list;
4. Expected to see on device1's list the device2 in approx ~15..35 seconds
5. Connect device3 to the sync chain, expected to see device1;device2;device3 on each device list in approx ~15..35 seconds.

[darkdh]

++

[kjozwiak]

Reproduced the original issue using the STR/Cases outlined via brave/brave-browser#27931 (comment) on Win 11 x64 using the following build(s):

Brave | 1.50.25 Chromium: 110.0.5481.77 (Official Build) nightly (64-bit) 
--- | ---
Revision | 65ed616c6e8ee3fe0ad64fe83796c020644d42af-refs/branch-heads/5481@{#839}
OS | Windows 11 Version 22H2 (Build 22621.1265)

Using a Win 11 x64 (Device A) machine and a Win 10 x64 VM (Device B), I reproduced the issue mentioned via brave/brave-browser#27931 (comment) where it took almost ~10-15min for the Win 10 x64 (Device B) machine to appear in the list under brave://sync via the Win 11 x64 machine (Device A). I went through the above a few times and consistently ran into the issue.

Example of Device B not appearing in Device A after 10-15min

Example	Example	Example

Syncing about 10-15min

---

Verification PASSED on Win 11 x64, Win 10 x64 & Pixel 6 running Android 13 using the following build(s):

Brave | 1.50.54 Chromium: 110.0.5481.104 (Official Build) nightly (64-bit)
-- | --
Revision | 46de4a7f41979e829b430bc1ee30ef483aa227ac-refs/branch-heads/5481_77@{#19}

• Win 11 x64 - Desktop - Device A
• Win 10 x64 - VM - Device B
• Pixel 8 running Android 13 - Device C

Using the same STR/Cases I ran through the above with the guidance of #17077 (comment), ensured that Device A, Device B and Device C all appeared via brave://sync within ~15s-1min rather than the previous ~10-15mins.

Example of Device A, Device B & Device C appearing in brave://sync within 1min on Desktop

Example of Device A, Device B & Device C appearing in brave://sync within 1min on Android

Example	Example

I also ensured that import1 & import2 folders were being synced between the three devices. Sometimes this took a bit of time but assuming it's because how large these bookmark files are. However, they always eventually sync even though it takes a bit of time. But the devices get added within ~1min which is a huge improvement compared to the previous ~10mins or more.

[cdesouza-chromium]

.