Is it my job as solution architect to learn all these laws and see how they apply to the software we are going to make or should this be a task for somebody else?
If you don't want to learn the laws, you are basically asking to receive complete requirements with everything perfectly laid out for you, so that in turn, you can then lay out a technical solution. Even if you do get everything handed to you, you still need to understand it all, otherwise you have no guarantee you will be building the right thing (until it gets rejected by quality control or testing, which isn't very efficient or effective).
In heavy regulated environments, the company usually has a legal and/or compliance department that makes sure things get respected and implemented accordingly, but everyone involved in building the solution needs to know what they are doing. Developers and architects need to know the business domain, which in this case involves learning about some laws.
Danny Schoemann gave a nice car example in one of his comments, so I'll give another car related example: as a taxi driver, do you need to learn the city you are driving in, or do you just handle the car and expect the GPS to tell you where you need to go?
So yes, you need to learn the laws. The question isn't if you should learn them, but how much (or to what level of detail) you should learn them, to which the answer is: enough to be able to do your job efficiently and effectively.