Search box should use search engine settings

[tanquang]

Currently the search list here is fixed, we will consider improving this feature in the future.

Also, when I remove the default search engines at "chrome://settings/searchEngines", it will be saved to the "User Data\<USER>\Web Data" file. However, for some reason, this "Web Data" file will cause the passkey feature of the Bitwarden extension to work erratically after every browser restart. But simply deleting this "Web Data" file will make the Bitwarden extension work normally again.
I hope you also move the data when removing these default search engines to another file.