Highlighting text in a page and selecting "Search Web" opens Safari

Description of the issue:

In iOS and iPadOS highlighting text in a web page and selecting “Search Web” opens Safari and performs the search there, even though I have Brave set as the default browser.

Is there a way to force the iOS to perform the search in Brave, just as it does in the Windows desktop version?

Brave Version (check About Brave):
1.45.2 (

Operating System:
iOS/iPadOS 16.2