I want to know who collects all necessary administrative data in US state governments, is any particular office, or director responsible for handling, disseminating, and analyzing data? Also, are executive departments of the US government responsible for collecting state data?
Each state in the US runs their governments differently; while there may be similarities and/or overlap between them, I'm going to go ahead and say that there are 50 different versions of who collects necessary administrative data in US state governments.
Adding to the 50 different versions, I'm not aware of any state that has any one agency/office/director that heads this up. Virginia has a number of state agencies, that all are responsible for collecting the data necessary/required for their functionality. In my experience, most of these agencies are run in silos and there is very little data sharing, so its more like 50 * X, where X is the number of agencies/directors/offices collecting data in each state.
Federal agencies of the US government collect data within states, but I'm not aware of any agency that is responsible for collecting data states should be.
COVID-19 has exposed many issues with US federal/state/local data collections, and I think can help illuminate the answers to what you are asking.
A few months into the pandemic, CMS.gov forced all Long Term Care Facilities in the country to start reporting their COVID data to CMS.gov.
This may seem like a federal agency being responsible for collecting state data, however the states did not stop collecting this data at the same time. There are a few reasons why this was done, but the primary reasons being that each state's process/data collection was unique (no standards), and some states were simply not sharing their data with the public.
So we are left with 51 versions of the data collections; 50 state flavors + 1 federal flavor.
There have been a number of initiatives to get governments to be more data driven/digital in recent years, and the one that stands out to me/could be related here is the emergence of state CDOs (Chief Data Officer). However, I don't think any of these offices are doing what you are asking, at least not yet. If there is one, it would probably be California; I am familiar with Virginia's, and its not 100% clear to me what our CDO's role is and/or what they are accomplishing. That said, I can affirmatively state that Virginia's CDO is not doing what you are asking.