How do added tasks/stories affect story point estimation and Agile Sprint planning?
Example: 13 point story but only when you start the work do you realize new tasks/stories need to be added to the sprint (as part of that story/topic).
You may want to consult the Scrum Guide here:
"If the work turns out to be different than the Development Team expected, they collaborate with the Product Owner to negotiate the scope of Sprint Backlog within the Sprint."
If the estimation needs to be updated in this context, the development team should do so.
> 13 point story but only when you start the work do you realize...
I'd say that in Scrum the appropriate choice of word would be "and" rather than "but" i.e.:
"13 point story *and* only when you start the work do you realize..."
This is because ongoing changes to a Sprint Plan are very much to be expected. Daily Scrums are a regular opportunity for the team to meet and replan in order to achieve the Sprint Goal. This includes the replanning of tasks and the updating of estimates. The Development Team should also be prepared to meet with the Product Owner in order to revise the selected PBI's if this helps to preserve the agreed goal.
Remember that Scrum was devised to create an empirical approach to complexity. We continually uncover unknown or unexpected; Scrum helps us do that early rather than too late.