Context - how to set and keep in composer

This is an elementary question, but I can’t seem to find the answer.

What is the proper way to set the context for composer. Today in my discussion with Claude I found that it did not have the context I thought that it had.

If I drag a folder to context should all files in the folder be in context?
Should all sub-folders and files be in context?

I think yes, but it seems the answer is no. Or perhaps this is a bug. It seems that the composer is quickly forgetting the files I add to context.

When I add a file or folder, should they be accessible (able to see the existence of the file, as well as able to see the contents) for the duration of the session?