The type and location of records for persons who served during the Spanish American War is going to be different depending on what branch they served in (Army, Navy, or Marines), and whether they were officer or enlisted. For Army personnel, it will also depend on whether they were Regular Army or from a volunteer unit.
The National Archives article "Sailors, Soldiers, and Marines of the Spanish-American War" provides a description of the types of records available for each category of serviceman. https://www.archives.gov/publications/prologue/1998/spring/spanish-american-war-2.html
The National Archives Identifier (NAID) that you give corresponds to the record series Carded Records Showing Military Service of Soldiers Who Fought in Volunteer Organizations During the Spanish-American War which can be found at this link: https://catalog.archives.gov/id/300400
This catalog description does NOT contain a complete online list of all persons serving in the military during the Spanish American War. Instead it contains service records of those persons who served in volunteer units. Some of these service records have been digitized are searchable through the following link, however not all the files have been put online yet: https://catalog.archives.gov/search?q=*:*&f.ancestorNaIds=300400&sort=naIdSort%20asc
There are other record series for other categories of service members, such as the Enlistment Papers, 1798 - 10/31/1912 (https://catalog.archives.gov/id/300390) which has service records of men enlisted in the Regular Army, however most of those are not name searchable.
Your easiest option would probably be to order a copy of your great grandfather's service record from the National Archives using the procedures outlined here: https://www.archives.gov/veterans/military-service-records/pre-ww-1-records
All of the military service records from this time period are at the National Archives in Washington DC. Their contact information is here if you want to speak to them directly: https://www.archives.gov/dc
Finally, some quick advice about searching the National Archives Catalog.
The link to the Catalog is here: https://catalog.archives.gov/
If you already have a NAID, which is a unique identifier for a description or authority file in the Catalog, you can often simply search for that number and the first result will often (but not necessarily) be the record series, file unit, or item which that NAID refers to. Also, using an advance search (https://catalog.archives.gov/advancedsearch ) you can enter the NAID into either "Search Term" or "Description Identifier" and it should come up with results. Of course, you can also search by key words, and with the advanced search you can filter by type of records, dates, etc.