When using chrome and select/look up text to search, goes to Safari

Whenever I am using the chrome browser within the iOS operating system, and I select text to look up, instead of searching within chrome, I am taken to a small intermediate search box. This generally always says "no contents found". When I select "search web" in that box, it always takes me to search results in Safari. If I wanna go back to Chrome, I need to click a few more buttons to get it to search in the right place. This happens every time when using both my iPhone, and my mini iPad, both using the most current iOS, and both the most recent model type.

This has been happening for years and I always assumed it was simply a decision on Apple's part to preference safari over chrome. Is this the case? Or am I permitted to use Chrome within chrome?

Thank you