You have the new Microsoft Edge browser (built on Chromium), and you’d like to have it automatically purge your search history every time you close your browser. You can have it remove more than just your search history. Edge can clear browsing data of various kinds automatically. No fluff in this post. Here’s how you do it…
Click the “3 dots” button, then click Settings

Note: Depending on your screen size, you may see a different versions of these screens. I’ll include those screenshots and descriptions here, too.
Click Privacy & Services then click “Choose what to clear every time you close the browser.”

For smaller screens, click the hamburger menu next to “Settings”

For smaller screens, “Privacy and services” is under the hamburger menu

Under “Clear browsing data” select the items you want to clear

Once you’re in “Privacy and services / Clear browsing data on close“, simply click the toggle switches on the right side to enable/disable the items you would like to clear every time you close Microsoft Edge.
Here’s an example of the option, “Browsing history” set to delete every time you close Microsoft Edge. This also removes the autocompletions of things you’ve typed in the address bar.

Microsoft Edge was recently updated on many computers, unbeknownst to many users (probably your story, since you’re here). Love it or hate it, this is technology, and SOMETHING will always be changing. I hope this article has been helpful to you.
Let me know if this article helped you or not. Reach out and let me know what other questions/problems you may have.
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Hey, I followed your directions and will see if it works. When I go to History after clicking Close, it should then be empty, right? I clicked the first two toggles.
Yep, that should be the case. Let me know if you see anything different.