When you got the visa you have to show nothing any more, bc you won't handle anything with embassy or Imigration, everytime you enter Thailand you will get 180 days, no extention required
a state can't offer a permission to work for a company outside the state or can deny it. It's possible only for their state territory. So it's not illegal to sit with a laptop somewhere and write a report, do a project, write a song, programm an app aso. It's only relevant to Thai law if you do it for a Thai company inside Thailand. And all the stories are bullshit and lies. Nobody got ever arrested when working remotely