Impossible to install the module due to the wrong 'core' value in the search_kint.info.yml

#2 patch applied cleanly.And module installed without errors.

This is related with the patch in https://www.drupal.org/project/search_kint/issues/3120060, which looks correct, but probably something has been missed during a conflict resolve.

Is the problem here that core should just be 8.x and core_version_requirement should be ^8 || ^9 like the example here?

Here is what there currently is search_kint.info.yml

it looks good to me
drupal-8.8.1 % vendor/bin/rector process modules/contrib/search_kint --dry-run
Rector 0.8.x-dev@8896f0a
Config file: rector.yml

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[OK] Rector is done!

drupal-8.8.1 % vendor/bin/drupal-check -ad modules/contrib/search_kint
PHPStan crashed in the previous run probably because of excessive memory consumption.
It consumed around 53 MB of memory.

To avoid this issue, allow to use more memory with the --memory-limit option.
Warning: Class 'PHPUnit\Framework\MockObject\Matcher\InvokedRecorder' not found in /Users/Documents/standar_drupal/drupal-8.8.1/core/tests/bootstrap.php on line 197
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[OK] No errors

Fixed and pushed.