I guess I don't understand what PRIIA has to do with anything. PRIIA is not an appropriation bill, and the PRIIA 209 changes outlive PRIIA. They are perpetual until and unless rescinded by another bill.
Perhaps someone who understands the legal nuisances can step in here and provide a more accurate summation,
It is traditional, for reasons I do not understand, for the federal government to provide money by a two-step process, first "authorizing" the appropriation of money, and then appropriating the money.
This is not necessary. Congress can authorize-and-appropriate in a single bill. The appropriations are the important part.
It is also traditional for Congress to authorize "up to" some amount, and then to appropriate a particular amount. This is *also* not necessary. There are certain agencies which have authorized and appropriated "such sums as are necessary" for particular tasks in perpetuity. Notably, the Treasury Department has several such appropriations, including the one for paying interest on federal debt instruments and the one for minting coins.
So, in short, in order to get funds, all that is needed is an appropriations bill; everything else can be wrapped into the appropriations bill. There are agencies which operated off nothing but yearly appropriations bills for decades.
Authorization bills and all that are just decoration; they consist of Congress purporting to regulate Congress's behavior, but Congress has no actual power to restrict the actions of future Congresses.
Regarding PRIIA, most of the PRIIA rules are permanent law, and they changed the law *regulating* Amtrak. So until they are repealed or changed, Amtrak has to follow the rules, regardless of appropriations.