A client pauses a contract when the pay want the freelancer to stop working on the project... at least temporarily. The client may unpause the contract soon. Or tomorrow. Or never.
If a client pauses my contract, I usually just work on other projects until the client unpauses the contract. It is their project and their money. So they may pause at any time.
Upwork suspends a contract when there are issues with the client's payment method. When this happens, I wait until the contract is unsuspended before I resume working on the project.
Either way, I don't send a message to anyone. I just wait until things are back to normal.