Search form vs. unified search in a web application

I am looking for some help regarding UX/design guidelines targeted at (web) application internal search functionality. I have tried searching the Google and this site, but the overwhelming majority of information available has to do with guidelines for search functionality in content-based websites, which is not the same thing.

Below is an example of one of the search forms available in our application (datepicker format is wrong because of legacy controls, and the translations on the controls are not the best ever, but try to make do).

To get to the point, what is the current general opinion of search forms like this, with perhaps additional criteria hidden behind an "advanced search" expandable panel vs. a single search field applied to all relevant database fields, with search results sorted and ranked according to some sensible logic (exact matches higher than partials, etc.)? With the second option, more detailed criteria fields could be offered either under "advanced search", or then if the search results produced too few/many results.

We do not have any statistics currently on usage behaviour, as that was not considered by whoever made the previous version. The plan is to include statistics in this remake, so we have better information available for the next version.

TLDR: Search form with multiple fields vs. unified single search field. Current direction of application design, preferably with some research/documentation as evidence?

Thank you in advance for your help.