Is there a screen that shows all military and mining stations in Stellaris?

There is no such aggregate management window for your military stations. However, with the changes that came in the 2.0 update for Stellaris, you now have "Shipyards" instead of military stations. You can view a list of these Shipyards at a glance in the Outliner window on the right-hand side of the screen:

The red arrow on the photo indicates the section (each section is collapsible by clicking the section header) where your new military outposts (called Shipyards) are listed. The orange puzzle piece icon (circled in red) indicates that there are available modules or buildings that can be constructed on that Shipyard.

When an existing module or building on a Shipyard can be upgraded, an orange 'up' arrow will appear next to where the orange puzzle piece icon (see the arrow next to the Mithar Prime planet in my screenshot, for example). Clicking on any of these orange icons will open the individual Shipyard management window where you can view all the details you would like.