You can turn on "advisors suggest retrofits." Whenever you see the retrofit suggestion pop up, pause the game, redesign everything you want to be upgraded, and then accept the suggestion and resume playing. All ships and stations will be ordered to retrofit to the most recent nonobsolete design in the appropriate role when the advisor suggestion is accepted. Ships or stations which are already of the most recent nonobsolete design will not be ordered to retrofit. Be warned that this can screw things up if you're trying to run multiple designs within a single role, as this form of mass retrofit will upgrade all ships or stations of the same role to the same design.
Assuming the Retrofit column in the design menu shows "automated" in the line for that particular design, the computer will (eventually) order stations and automated ships to retrofit to the most recent design, but these retrofits tend to be staggered (most likely to minimize the instantaneous impact on cash on hand) and may be postponed if the computer feels that your empire does not have enough cashflow to afford the upgraded station.
Go into the Ships and Bases menu to order mass retrofits. Filter using the drop-down menu and sort by clicking on one of the column headers (clicking the blank header on the far left and then changing filters restores the list to default sort, which appears to be by how recently the ship or station was ordered) to make finding things easier. You can select multiple things simultaneously here with shift-clicking and cntrl-clicking to issue orders for mass retrofits to nonobsolete class of your choice in the role of the things selected, if you want everything selected to upgrade to the same class and have only selected vessels of a single role (I don't recall how it works when you have ships or stations of more than one role selected).
I don't see much practical difference between the "Edit" and "Manual Upgrade" buttons on the design screen, so it'd sure be spiffy if the prompt option were there (where I could highlight the design and select to update all of that design).
"Edit" is there for checking what's on current designs which you do not want to upgrade or for making changes to a current design which is not yet in service without changing the mark number, "Manual Upgrade" is for when you want to upgrade a class which is currently in service.
For example, on a prewarp start, you might ensure that all Generation 2 (Mk2) ships have Gerax Hyperdrives, Fission Reactors, Standard Armor, Corvidian Shields, and Tier 1 weaponry (Maxos Blasters, Epsilon Torpedoes, Concussion Missiles, Rail Guns), all Generation 3 (Mk3) warships have swapped Ion and Directional Thrusters for Proton Thrusters and Thrust Vectors, Generation 4 (Mk4) warships have assault pods, etc. This can be useful for bookkeeping.