It seems there are multiple reasons why this could happen. I tried to run other apps on my simulator, restarted my simulator and even tried to delete the build folders and rebuild from scratch, but none of these approaches solved the issue.
What finally worked was restarting the React Native Debugger that I had on in the background the entire time.
You can also check the Network tab of React Native Debugger if you’ve enabled Offline throttling. Disabling it should also solve the issue in some cases.