Make sure end-to-end tests use unique filenames in template tests

What does this MR do?

1. Don't assert on flash presence since flashes aren't reliably shown and are only informative messages. This MR stops asserting against the flash message and only asserts against the presence of the file on the page instead.
2. In the case an error occurs during the file creation process, but after the file is created, the retry of the example will now fail before creating the new file since a file already exists with the same name. This MR makes sure the file created has a unique name each time.

Closes #210504 (closed), #227029 (closed).