Post page–no sidebar?

I have a posts page, which is not my homepage. It shows posts in boxes and if you click on one, you’ll see the post itself, with a right sidebar that I set up that has categories, archives, etc.

Is there a way to get this right sidebar on the posts page itself? When I edit the page, there’s no option to make it full-width or have a sidebar like there is on other pages. It seems odd that on the page that actually displays the list of posts, you can’t search or look at particular categories. Am I doing something wrong?