Instant Search: ensure the hidden overlay doesn't add whitespace to printed pages

[bluefuton]

Fixes https://github.com/Automattic/jpop-issues/issues/7134.

Note: this PR is branched off #21637.

The only confirmed theme that this has happened on is 'Field Guide' but there may be others.

Changes proposed in this Pull Request:

Ensure the search overlay is completely hidden on printed pages.

On certain themes, the overlay's presence can cause blank pages to be added to the printout.

Does this pull request change what data or activity we track or use?

No.

Testing instructions:

1. Open a site with Instant Search installed. Don't start a search.
2. Bring up the print preview for the page.
3. Ensure there are no extra blank pages added by the hidden overlay.
4. Inspect the print styles in the browser and ensure that 'display:none' is applied to '.jetpack-instant-search__overlay'.

[github-actions]

Thank you for your PR!

When contributing to Jetpack, we have a few suggestions that can help us test and review your patch:

• ✅ Include a description of your PR changes.
  
• ✅ All commits were linted before commit.
  
• ✅ Add a "[Status]" label (In Progress, Needs Team Review, ...).
  
• ✅ Add testing instructions.
  
• ✅ Specify whether this PR includes any changes to data or privacy.
  
• ✅ Add changelog entries to affected projects
  

This comment will be updated as you work on your PR and make changes. If you think that some of those checks are not needed for your PR, please explain why you think so. Thanks for cooperation 🤖

---

The e2e test report can be found here. Please note that it can take a few minutes after the e2e tests checks are complete for the report to be available.

---

Once your PR is ready for review, check one last time that all required checks (other than "Required review") appearing at the bottom of this PR are passing or skipped.
Then, add the "[Status] Needs Team review" label and ask someone from your team review the code.
Once you’ve done so, switch to the "[Status] Needs Review" label; someone from Jetpack Crew will then review this PR and merge it to be included in the next Jetpack release.

---

Jetpack plugin:

• Next scheduled release: January 11, 2022.
• Scheduled code freeze: January 3, 2022.

[kangzj]

When I change rendering to print, the style is applied correctly:

And the change seems safe to me, so feel free to merge when you are ready 👍

[jsnmoon]

Works as described!

The base branch was changed.

[bluefuton]

Will create a fresh PR branched off master instead of trying to navigate this rebase mess.