I can confirm the guide’s branches cost 0 actions on the web version as well.
Glad to see your problem got resolved and you can continue.
If this means that you’ve never used the cards mechanic before (i.e. even outside the Flash Lay), this is a good opportunity to get to know your opportunity card deck better - much of Fallen London’s content comes in the form of opportunity cards, and not just pinned storylets. In fact, some storylines rely on waiting for the right opportunity to arrive (in the form of flipping cards occasionally and hoping for the best).
Some cards are location specific (i.e. you can only draw them in certain areas), some are situation specific (i.e. depend on certain qualities, attributes or items), and some are universal (there’s always a chance to draw them).
Have fun, and don’t hesitate to ask the community if anything seems unclear!