[Bug]: Unable to Set Custom Search Engines or Extension-Based Startpages as Default

[Juhayer-Al-Wasif]

Version

0.8.4.1

Have you tested that this is not an upstream issue or an issue with your configuration?

• I have tried reproducing this issue in Chrome and it could not be reproduced there
• I have tried reproducing this issue in ungoogled-chromium and it could not be reproduced there
• I have tried reproducing this issue in Helium with a new and empty profile using --user-data-dir command line argument and it could not be reproduced there

Description

Unable to Set Custom Search Engines or Extension-Based Startpages as Default

How to Reproduce?

Go to https://search.brave.com
Check Search Settings for brave serach to appear
But there is no option for brave search.

Add Startpage extension
Check Search Settings for startpage to be set as default.

Actual behavior

There is currently no functional way to set Brave Search as the default search engine, nor can a custom Startpage extension override the default New Tab page. The settings either do not provide an "Add" button for custom engines or fail to respect the extension's request to manage the home page.

Expected behavior

By visiting https://search.brave.com should give an option in search settings to add the search engine, which is not the case.
By adding the extension of startpage should automatically make startpage default seach engine, which is also not the case.

Additional context

No response