The requirement to notify will be in the severance agreement. They don't forbid another job. They want to encourage people to get new jobs so they can pay less for disposing of you. You're right that severance previously was in lieu of filing a legal dispute. They've changed their terms. They know most don't sue because suing costs money and they have more resources.
One thing to do is delay updating any professional profiles like L***n, and don't share details until you're done with severance. If we all do this, it will make trying to collect back money very hard and expensive. The contract clause is an immoral clause because it is non-negotiable. It is designed by people whose compensation is based on cutting costs to make the company look attractive to buyers. The same cost strategy was used by KR in her last role - do an internet search and you'll see the impact.