Handle TemplateNotFound to render more helpful error message.

At the point the exception is handled, it is likely due to error loading
a sub-template included from main template. Besides file not found, it
can be caused also by include path failing Jinja2 checks. Now, when
rendering the exception from Jinja, it will include exception name. This
will give basic context or *what* the error is.

Fixes #7103
Fixes #7105