How to make blocks contextually aware of current webform page
This is currently not possible through the default UI due to the URL of all webform pages being the same.

There are two possibilities as far as I know.

(1) If your blocks only show help texts or any other static information, you should probably not use blocks at all but add markup components and place them after each page break.

(2) If you are indeed using dynamic blocks (e.g. coming from views), you would need to create a custom theme file (e.g. webform-form.tpl.php) in which you may enter the logic defining which block should appear. The currently viewed page number of your webform should be available through $form['details'].