I saw this in the OW core book - it's implied that at least Astropaths and bound Chaos psykers should have this. Are PC psykers supposed to have this as well?

Nope.

Soulbound means that such psyker's soul has been bound to another.

For Astropaths, the Emperor.

For Chaos Psykers, demons.

For astropaths, this allows them to communicate to each other through their shared soulbind. This also helps prevent daemonic possession.

For chaos psykers, I am unsure.