Patch is not needed for HawkSearch_Connector extension starting from 2.5.4 version
HawkSearch_Connector extension version 2.4.* - 2.5.0 uses Laminas library which isn't supported by Magento below 2.3.5 version. For the purpose of providing new updates for customers who have Magento stores on versions 2.3.0-2.3.4-p2 Magento store owners need to install "hawksearch_connector_2.4_magento_2.3.0-2.3.4-p2_compatibility_patch_cli.patch"
Since "hawksearch/connector" composer package of version 2.4.* doesn't support Magento 2.3.0-2.3.4 it is not possible to use composer installation for HawkSearch extension package on that Magento version. Please install HawkSearch extension package from via files in app/code folder and then apply the patch.
Download the patch file and apply it using one of commands bellow
patch -p1 < hawksearch_connector_2.4_magento_2.3.0-2.3.4-p2_compatibility_patch_cli.patch
git apply hawksearch_connector_2.4_magento_2.3.0-2.3.4-p2_compatibility_patch_cli.patch
Read more about applying patches