if you want a point for every cell in the DEM, is the Raster to Point tool. A point will be created at the center of every cell with an attribute that is the value of that cell.
If you don't want every cell, you first need to use Create Fishnet to generate the grid. Where you define the cell size, Once you have the points, you can use the Extract Values to Points tool from Spatial Analyst as you mention to get the elevation values.

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