First Things First! "Dataverse search helps you quickly find what you're looking for. It delivers fast and comprehensive results across multiple tables in a single list, sorted by relevance"
Now here is the key bit "Dataverse search is an opt-out feature, set to On by default with 2021 release wave 2, on all production environments, except those using their own encryption key."
So if you run into issues related to global search after release wave 2, you know why. Because your table / entity maynot have configured for Dataverse Search.
Please refer the below Microsoft Link to see how to configure the dataverse search in detail. Mainly need to set up search indexes.
https://docs.microsoft.com/en-us/power-platform/admin/configure-relevance-search-organization
