Problem is that you are merging 2 different things.
-admin 2 or admin 3-4 means administration level, in the following link you have acomprehensive description of different admin level and if they are included in some level or not.
-zoom levels and vector tiles in Mapbox.
In some layers (if the data is there) zoom level displaying is limited by a filter, in mapbox you have for each layer a Style and a Filter tab.
When you open filter tab you'll see what data is visible at that level and you can change this, for example some small streets are limited to only appear when you are at zoom level 13.
Vector Tiles, vector tiles is the format mapbox stores and uses data, it's similar to raster tile schema (data is packaged into different zooms and is generalized for lower zooms), so algorithm that packages data into vector tiles don't include all data at all zoom levels.
So, for zoom 0-2 probably you only have land and water and some names, and boundaries to the others.
go to natural earth data,
zipp shapefile you need admin-0-boundaries (polygons or lines) lines are only inland, no coastline.
upload to mapbox as TILESET
ADD A NEW LAYER, select uploaded tileset and start styling.