how to remove the large spotlight search box on Mac Sequoia

It had to be something under Accessibility!

System Settings->Accessibility, click "Hover Text" and turn both settings there OFF:

Have not heard of this mystery Second Screech box that occupies " a large portion of the screen real estate "

To drill down on this issue and avoid a " Game of 20 Questions "

Download the Application Etrecheck ( External Link ) directly from the Developer.

This is a Diagnostic Tool that makes no changes to the computer.

It makes a coherent and readable inventory of both the Hardware and Software used on the computer 

The application is free or paid for added features. 

The Report will Not Reveal Any Personal Information. 

Post back the Full Report - Share Report >> Copy , then  paste  >>>> using the Additional Text Icon  <<<<

I’ve seen that myself, not sure what it is, might check Siri prefs.

What follows in below may not be technically related to thisSearch Bar issue

Though, it should be considered carefully

Low disk space - This computer is running critically low on free hard drive space.

 disk0 - APPLE SSD AP0256Q 251.00 GB (Solid State - TRIM: Yes) 

Size: 245.11 GB

 Free: 39.19 GB

  Available: 90.07 GB

From another contributor @etresoft regarding Free Space and Available Space 

Free vs available disk space huge differe… - Apple Community

Quote >>  “ The "available" storage is the amount of used storage that the operating system could automatically delete if it felt that it was really necessary. The "free" storage is the amount that you can actually use for something.

There are system processes that run in the background and automatically delete some of the "available" storage and convert it to "free". If you completely run out of storage, then those system processes will try a little harder. When you "delete" files you are just hinting to the operating system that you don't need those files anymore. The operating system will eventually remove them, but on its own schedule.

Certain tools will allow you to force the issue and manually clean up some of this storage and manually delete local snapshots. But that is only temporary. "  << End Quote 

Google Chrome

Short and unpopular suggestion for some

 https://chromeisbad.com

May consider an alternative www.brrave.com which is essentially Google Chrome without the Google baggage 

Refer to the Posting by Respected Contributor @ John Galt 

Application memory error on my MacBook Pro - Apple Community

Refer to the Posting by Respected Contributor @ Kurt Lang

etrecheck... Mac running slow - Apple Community

Perhaps if you provide a Screen Shot of the " almost screen-wide search box appears whenever a dialogue box is selected "

This may provide some insights and context

dexter_y_ximena wrote:

Unable to do a screenshot because the unwanted search box disappears when I select "Capture" on the screenshot dialogue.

Just press command+shift+3

Aha, I think that is the Browser’s search bar, not the one you get to by clicking on the spyglass.