The biggest change after Honor's death are the Bondsmiths, The Stormfather in particular, as he himself notes.
Beyond that, I think Honor commanded spren to choose their Nahel Bonds more wisely, regulating it. Now, all people have to do is convince a spren, and though spren are attracted to certain qualities that are commonly accepted to be good, they are sapient beings, free to choose whom to bestow the power of the Surges upon. We see that the Oathgate spren are still bound by their word to him.
Shardblade and Shardplate seem to be based on the level of Ideals sworn, we simply haven't seen the main cast progress that far onscreen.
As for Soulcasting, it very well may have been safer in the Cognitive Realm when Honor was alive, but I don't think that the system of Soulcasting itself was affected by the Splintering.