Please allow settings parameters to be submitted in GET request - improves the mobile query url when private tab in use

Description of the issue:
When navigating in a private tab of a mobile browser and having configured Brave as a search engine, I type the text to query and receive a theme light response, when I would like a theme dark, and unfortunately I cannot pass it as a parameter in the GET request ´&theme=dark´

This URL should work:

Additionally, all parameters from settings should be accepted as part of the URL (language, locale, etc…)

Examples from competitors:
SearchX has a great settings page that generates URL passing a hash for the settings created (nice to have) that can be copied and pasted easily:

DDG has a knowledge base article explaining the parameters and its domains:

Nice to have
The knowledge base article Set Brave Search as default should explain this to the users.

(annoying that on a desktop I cannot get the mobile version of this KB article)

Operating System:
iOs with Firefox in Private Tab