It’s been said that season 2 of Picard and 3 of LD will be on Prime. Prime must have a different deal on those shows
Not necessarily. For all we know they could have a very similar contract.
We don't know Netflix and CBS, contracts terms. It might have a set number of years before a separation can be requested or initiated. If that is the case, its possible the one with Amazon could as well. But since those deals were initiated years later, then it would delay any possible separation. The separation terms could also require agreement by both parties. And there are certainly reasons why Netflix and Amazon might have different reasons on agreeing or refusing a separation. For example you might have a separation agreement that stipulates how much its going to cost, but still give the other party the right to opt out of it, or delay it for an already agreed upon period before it took effect.
For 10 years I worked as an accountant for a California farming company. It entered into an agreement with two other companies to develop the commodity that would be called "Cuties" (Clementines, hybrids of navels and mandarins). And while there, one of the parties initiated separation terms. These are far, far smaller companies (though the deal was in the tens of millions), and there were a host of various conditions. You had to give two full quarters notice to initiate separation. You could request a full buy out (which had to be approved by the other two parties), you could request separations of assets but keeping your share of the trademarks, and you could request the other parties buy you out. While obviously owners and controllers were aware of the situations, and probably discussed it with others, the staff wasn't allowed to speak to anyone outside of the engaged parties (we even had to sign new non disclosure forms during the process). And each of the two parties had up to the last two weeks, to give the sign off or deny the terms, which then took it down a different path for separation). The party that wanted out, requested to keep the rights to the trademark (so all three companies could still grow, produce and market the product under the name "Cuties"). That was rejected, they went through the various other subsections of the separation agreement, finally getting one that was agreed by all three parties, and it was signed and official about 2 weeks before the end of those two quarters.
This impacted lots of suppliers, and venders, staffing agencies, and company employees. And most got about 5 days of actual notice. And that's with a process that was designed to be covered in a period no longer than 6 month. That other company now uses the name "Halos' for their product.
I could not even hazard a guess on how easy or difficult this process is for significantly larger companies.