Tthe Measurement tool in the current ArcGIS Online Map Viewer does not have the same layer-snapping capability that many users relied on in Map Viewer Classic.
I checked the current Map Viewer measurement documentation, and it describes creating distance and area measurements, but doesn't mention any option to enable snapping to layer vertices or edges. In contrast, Map Viewer's Edit and Sketch workflows do have documented snapping controls and allow you to choose which layers to snap to.
Snapping while measuring is available in ArcGIS Experience Builder, with both the Map widget's Measure tool and the standalone Measurement widget snap to feature vertices and edges by default.
If you'd like this added to Map Viewer itself, there's an active request on the ArcGIS Ideas site worth supporting, as Esri prioritises ideas by community demand.
