While using mysql as a back end, the contexts aren't getting saved to the database, which causes the contexts to be lost on the next reload/restart.

+1

They also don't seem to have any effect while they are still in memory. After reloading or restarting, the permissions are still there, but with the context.

Actually, I can't seem to find any references on how to make contexts work period. Is [world=myWorld] not a recognized context?

Unfortunately PermissionsEx is currently unmaintained and no further updates are planned. Because of this, all pull requests are being closed. If you are looking for an actively maintained permissions plugin, take a look at LuckPerms. It is compatible with major server platforms and can import data from PEX.