Shortcut G instantly makes mouse movements Move the selection.
Is there a way to activate the Move tool without it instantly going into this button-less move state?
Similarly for Rotation and Scale.
G activates grab/move/translate operator. Operator only works with this operation that starts when the operator is called. If you want to use a tool with a move gizmo, you have to select the tool from the Toolbar:
The hotkey combination to activate the tool is Shift + Space -> G . Shift + Space calls the menu with all the tools and G selects the move tool from it.
If you are coming from another software and are more used to gizmos, I would like to encourage you to explore the way Blender works with the operators as well. You can off course use gizmos if you like and there are good use cases for them like for example they are probably more convenient for animating stuff, but the operators are very powerful and convenient once you get used to the way they work. You get Numeric Input functionality with them as well.
G
once just in your mind and press it actually when you would want to press the second button. $\endgroup$