Set flash error message only for current request when updating project

What does this MR do?

This fixes a flash error message from being shown twice when updating a project fails. The flash message was set for the current and next request. Now it's only set for the current request, thus only shown once.

Are there points in the code the reviewer needs to double check?

Why was this MR needed?

Requested in #43772 (closed)

Screenshots (if relevant)

Does this MR meet the acceptance criteria?

• Changelog entry added, if necessary
• Documentation created/updated
• API support added
• Tests added for this feature/bug
• Conform by the code review guidelines
  • Has been reviewed by a UX Designer
  • Has been reviewed by a Frontend maintainer
  • Has been reviewed by a Backend maintainer
  • Has been reviewed by a Database specialist
• Conform by the merge request performance guides
• Conform by the style guides
• If you have multiple commits, please combine them into a few logically organized commits by squashing them
• Internationalization required/considered
• End-to-end tests pass (package-and-qa manual pipeline job)

What are the relevant issue numbers?

Closes #43772 (closed)