It looks like what you want is just to move the inner face in the top image upwards?
So usually with it selected you only need to press G then Z to make sure you are moving on the Z axis.
If the second image is what happens if you do it like this, then because you probably first tried to extrude it with E, saw that it is not what you want and aborted the action with Esc or right-clicking.
The problem is: the extruding consists of two combined actions, first creating a connected duplicate of the face and then moving it (or rotating or scaling if you press R or S while the Extrude tool is still active).
Cancelling the action now only aborts the movement, not the creation of the duplicated face. So if you first tried to extrude and then tried to just move, your selection is now the newly created face and you move that upwards.
When you do not want the extra face(s) from an extrusion which you already started, you have to undo the action after cancelling it by Ctrl+Z. Or you can select all with A and then hit M > Merge > By Distance to merge the duplicate face(s) into the existing.
By the way, if the first image is the result of the Bevel tool, then you most likely have scaled your object to be wider and flat in Object Mode without applying the scale afterwards. Which means, the bevel distance is not even on all axes. To apply the scale, select your object in Object Mode and press Ctrl+A. If you do this before using the Bevel tool then the angle would have been already steeper immediately while beveling.
