"prompt for user input" but make it look like "search the web"

Here is an option, if I'm understanding your desire.

You can use a Trigger Macro by Name with a parameter and do anything you want.
I did a post about this a few years ago: Trigger Macro by Name Action - Passing Parameters Part 2. This action uses the Trigger Value to pass that parameter. In the link above, this is the important line: Passing Parameters

You can pass parameters (v8+) to the macro via the %TriggerValue% token by adding // and then the parameter to your search string. The //and anything after that will be ignored in the search.

I use it to tag, to search, to journal, etc.

Even though this is a web search that I'm showing below, you can still use it for other instances. This one I'm showing how to search for a topic or images of a topic. The macro is included in my identified post.

ScreenFlow

Bottom line, if you want something quick to enter a parameter, Trigger Macro by Name and using the //{variable/parameter} is an option.

I hope this helps, if not, please disregard.

KC