Alright, I think I figured it out!
I did a fresh install and only used two mods, Tantares and Bluedog Design Bureau. I noticed in game that the Tantares agency was showing up properly on the contracts menu but BDB's agencies were not, so I decided to check out the differences between the two agency CFG files. It seems that the Tantares agency CFG has one additional parameter that the Bluedog CFG did not.
In the Tantares CFG, right above "description = " is a parameter called "title = " with the same text found after the "name = " parameter. Adding the "title = " parameter to the BDB agency CFG file and using the same text from BDB's "name = " parameter caused the Bluedog agencies to properly display in the contracts menu.
I think my suspicions earlier were correct and something was changed after the KSP 1.3 localization update, causing mods that do not use the "title = " parameter to not display the agencies properly. To fix this issue is fairly simple, just add the "title = " parameter with copied text from "name = " to any agency configs that do not have it, although this is pretty annoying and likely time consuming if you have a lot of mods, but it is good to know that it can be fixed.
I hope that helps! Let me know if that works for you, and I think you are right, this is probably a common issue that most people don't notice since it is pretty minor and doesn't really affect gameplay.