Apple Mail search box is missing after upgrade to Catalina?

Hello and welcome to Apple Support Communities, Phil!

I understand you're not able to search in Mail. I'd be happy to provide information to help you address this.

Make sure the Mail app is full screen so you can see the search option: Manage windows on Mac

"Maximize or minimize windows

On your Mac, do any of the following in a window:

• Maximize a window: Press and hold the Option key while you click the green maximize button  in the top-left corner of an app window. To return to the previous window size, Option-click the button again.
• You can also double-click an app’s title bar to maximize the window (as long as the option to do so is set to “zoom” in Dock preferences).
• Minimize a window: Click the yellow minimize button  in the top-left corner of the window, or press Command-M. 
• You can set an option in Dock preferences to have a window minimize when you double-click its title bar.

Most windows can be manually resized. Drag the window’s edge (top, bottom, or sides) or double-click an edge to expand that side of the window."

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