Add default search model

It would be really nice if, when using the search url(as a search engine in a browser, or through Unduck, for example) without a specific model, a specific chosen model would always be used, not the last used one.
It used to be always 2.5 flash, now its the last used one. Its quite inconvenient to accidentally spend a premium credit for asking a question to an image model because you didnt have a choice :(