[CR109]: Import bookmarks and settings modal do not get dismissed after importing bookmarks

[MadhaviSeelam]

Description

Bookmarks were successfully imported via new onboarding pages and via import bookmarks & settings modal. However, the modal doesn't get dismissed

Steps to Reproduce

1. Install 1.48. 61
2. launch Brave
3. click hamburger menu>>Bookmarks>>Import bookmarks and settings
4. select Microsoft Edge Profile
5. click Import

Actual result:

Bookmarks were added to the bookmarks bar, but the modal is not auto-dismissed.

Welcome.to.Brave.-.Brave.2022-12-16.18-17-22.mp4

Expected result:

When clicked on Import button, success message Your bookmarks and settings are ready dialog should be shown.

1.46.x (CR108)

Reproduces how often:

Easily

Brave version (brave://version info)

Brave	1.48.61 Chromium: 109.0.5414.46 (Official Build) nightly (64-bit)
Revision	6e36b77363ef3febbe792af680fa1367993ddcf0-refs/branch-heads/5414@{#709}
OS	Windows 11 Version 21H2 (Build 22000.1335)

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? Yes

Other Additional Information:

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

Miscellaneous Information:

@mkarolin @rebron @brave/qa-team

[mkarolin]

I think this may have something to do with the parallel importer and not firing the import-data-status-changed event that the Settings WebUI expects. cc: @nullhook

[kjozwiak]

The above requires 1.47.155 or higher for 1.47.x verification 👍

[GeetaSarvadnya]

Verification PASSED on

Brave | 1.47.161 Chromium: 109.0.5414.61 (Official Build) beta (64-bit)
-- | --
Revision | 846c6eff1c374cde417a9cdc44193545cc07f354-refs/branch-heads/5414@{#1030}
OS | Windows 10 Version 21H2 (Build 19044.2364)

• Reproduced the issue in 1.48.61
• Verified the STR from the description and ensured that once the bookmarks are imported the success message Your bookmarks and settings are ready is shown.