Fallout 4 script extender stopped working after the game updated

Both are options. F4SE puts out a new build for each game version, and it's usually not a long wait, but sometimes it is. The catch is that even once F4SE updates, every mod with its own .dll plugin needs updating too, so you can be waiting on several authors. Rolling back is what most heavily modded setups do. There's a downgrader patch on Nexus that takes you back to the version your mods were built for, or you can pull the old depot through the Steam console. After that set the game to only update when you launch it, and launch through F4SE rather than Steam's play button so it doesn't patch behind your back.