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There was quite the controversy around the F123 back in the day.
One thing to remember is that “commissioned” means built and on the water. You can see in the Der Spiegel article linked up above that the actual design work on the vessel itself was happening back in 87/88 which means the targeting system was probably designed in 85/86…and now the choice of 8" floppy doesn’t seem nearly so odd.
You nailed it. The contract was awarded in June of 1988 and the ship was being designed in 87/88. That means the targeting system was almost certainly designed in 85/86. A time when 8" floppies were still prevalent in Industrial, Commercial, and Military systems.