The Measure tool has been simplified from R2024x onwards.  You should still be able to select all the different types of entities as you could previously.  For example, selecting Center point in the new UI is the same as selecting Center of arc in the previous UI.  To select a Surface in the new UI, select Canonic geometries (if it is a planar-face/cylinder/cone/sphere).  For all other entities, select Any geometry in the new UI.

If you would prefer to see the list of selectable entities you were familiar with previously, then from Me | Preferences | Common Preferences | Parameters, Measures, and Units | Measures | Measure Creation, check Propose advanced selection filters