I did some testing and found the isBasemapLayer of a layer would only tell me if the layer was an ESRI basemap, not my own.
When I created a map, and examined it in the debugger, I found it has a mapType of BASEMAP.
This snippet lists the name and type of each map in my project.
I found this by looking in the map objects in the debugger. (Visual Studio Code in my case)
import arcpy
p = "K:/Taxmaps/taxmaps2.aprx"
project = arcpy.mp.ArcGISProject(p)
print()
map = project.listMaps(wildcard="*")
for m in map:
print("map:", m.name, " type:", m.mapType)
pass
Output from code:
map: Clatsop County B&W tiles type: BASEMAP
map: County Overview Map type: MAP
map: Map type: MAP
map: Main Map type: MAP
map: Section Overview Map type: MAP
map: Township Overview Map type: MAP