[TASK] Show result count in live search

Showing the result count can help users to understand the quality of the
search query.

Additionally the example is changed to work out of the box.

Resolves: #100029
Releases: main
Change-Id: I8460e24af2ea86dd5cf711c9b34768628d81e1c8
Reviewed-on: https://review.typo3.org/c/Packages/TYPO3.CMS/+/77944


Reviewed-by: Oliver Bartsch <bo@cedev.de>
Tested-by: core-ci <typo3@b13.com>
Tested-by: Oliver Bartsch <bo@cedev.de>
Tested-by: Andreas Fernandez <a.fernandez@scripting-base.de>
Reviewed-by: Thomas Hohn <tho@gyldendal.dk>
Reviewed-by: Andreas Fernandez <a.fernandez@scripting-base.de>